[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/7879#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/7879","headline":"Reed-Muller-Code  &#8211; \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"Reed-Muller-Code  &#8211; \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 Reed-Muller-Codes \u5b89\u5168\u306a\u30c7\u30fc\u30bf\u9001\u4fe1\u3068\u30c7\u30fc\u30bf\u30b9\u30c8\u30ec\u30fc\u30b8\u306e\u305f\u3081\u306b\u4e0b\u6c34\u9053\u306e\u9818\u57df\u3067\u4f7f\u7528\u3055\u308c\u308b\u7dda\u5f62\u306e\u30a8\u30e9\u30fc\u3067\u88dc\u6b63\u3055\u308c\u305f\u30b3\u30fc\u30c9\u306e\u30d5\u30a1\u30df\u30ea\u30fc\u3067\u3059\u3002\u3053\u306e\u30af\u30e9\u30b9\u306e\u30b3\u30fc\u30c9\u306f\u3001Irving S. Reed\u3068David E. Muller\u306b\u3088\u3063\u3066\u958b\u767a\u3055\u308c\u307e\u3057\u305f\u3002 after-content-x4 \u30d0\u30a4\u30ca\u30ea\u30ea\u30fc\u30c9\u30df\u30e5\u30e9\u30fc\u30b3\u30fc\u30c9\u306f\u3001Mariner Expeditions\uff081969\u304b\u30891976\uff09\u3067NASA\u306b\u3088\u3063\u3066\u3001\u706b\u661f\u304c\u64ae\u5f71\u3057\u305f\u5199\u771f\u3092\u5730\u7403\u306b\u9001\u308b\u305f\u3081\u306b\u4f7f\u7528\u3057\u307e\u3057\u305f\u3002\u7279\u306b\u3001RM\u30b3\u30fc\u30c9\uff081\u30015\uff09\u306f\u3001Mariner 9\u306b\u5236\u5fa1\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3092\u4f7f\u7528\u3057\u306a\u3044Hadamard\u30b3\u30fc\u30c9\uff0832\u30016\u300116\uff09\u3068\u3057\u3066\u4f7f\u7528\u3055\u308c\u307e\u3057\u305f\u3002\u3064\u307e\u308a\u30016\u3064\u306e\u60c5\u5831\u30d3\u30c3\u30c8\u304c32\u30d3\u30c3\u30c8\u306e\u9577\u3044\u5358\u8a9e\u3067\u30a8\u30f3\u30b3\u30fc\u30c9\u3055\u308c\u3001\u5358\u8a9e\u306e\u6700\u5c0f\u91cd\u91cf\u306f\u5c11\u306a\u304f\u3068\u308216\u3067\u3042\u308a\u30017\u30d3\u30c3\u30c8\u306e\u30a8\u30e9\u30fc\u88dc\u6b63\u3092\u53ef\u80fd\u306b\u3057\u307e\u3057\u305f\u3002\u3068\u3068\u3082\u306b 2 6 = \u516d\u5341\u56db {displaystyle 2^{6} = 64} \u30b3\u30fc\u30c9\u30ef\u30fc\u30c9\u306f\u3001\u30d4\u30af\u30bb\u30eb\u306e\u30b0\u30ec\u30fc\u5024\u3092\u30b3\u30fc\u30c9\u3057\u307e\u3057\u305f\u3002\u3053\u308c\u306b\u3064\u3044\u3066\u306f\u3001\u6b21\u306e\u4f8b3\u306eNASA","datePublished":"2019-04-09","dateModified":"2019-04-09","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/c4becc8d811901597b9807eccff60f0897e3701a","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/c4becc8d811901597b9807eccff60f0897e3701a","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/7879","wordCount":14166,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 Reed-Muller-Codes \u5b89\u5168\u306a\u30c7\u30fc\u30bf\u9001\u4fe1\u3068\u30c7\u30fc\u30bf\u30b9\u30c8\u30ec\u30fc\u30b8\u306e\u305f\u3081\u306b\u4e0b\u6c34\u9053\u306e\u9818\u57df\u3067\u4f7f\u7528\u3055\u308c\u308b\u7dda\u5f62\u306e\u30a8\u30e9\u30fc\u3067\u88dc\u6b63\u3055\u308c\u305f\u30b3\u30fc\u30c9\u306e\u30d5\u30a1\u30df\u30ea\u30fc\u3067\u3059\u3002\u3053\u306e\u30af\u30e9\u30b9\u306e\u30b3\u30fc\u30c9\u306f\u3001Irving S. Reed\u3068David E. Muller\u306b\u3088\u3063\u3066\u958b\u767a\u3055\u308c\u307e\u3057\u305f\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30d0\u30a4\u30ca\u30ea\u30ea\u30fc\u30c9\u30df\u30e5\u30e9\u30fc\u30b3\u30fc\u30c9\u306f\u3001Mariner Expeditions\uff081969\u304b\u30891976\uff09\u3067NASA\u306b\u3088\u3063\u3066\u3001\u706b\u661f\u304c\u64ae\u5f71\u3057\u305f\u5199\u771f\u3092\u5730\u7403\u306b\u9001\u308b\u305f\u3081\u306b\u4f7f\u7528\u3057\u307e\u3057\u305f\u3002\u7279\u306b\u3001RM\u30b3\u30fc\u30c9\uff081\u30015\uff09\u306f\u3001Mariner 9\u306b\u5236\u5fa1\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3092\u4f7f\u7528\u3057\u306a\u3044Hadamard\u30b3\u30fc\u30c9\uff0832\u30016\u300116\uff09\u3068\u3057\u3066\u4f7f\u7528\u3055\u308c\u307e\u3057\u305f\u3002\u3064\u307e\u308a\u30016\u3064\u306e\u60c5\u5831\u30d3\u30c3\u30c8\u304c32\u30d3\u30c3\u30c8\u306e\u9577\u3044\u5358\u8a9e\u3067\u30a8\u30f3\u30b3\u30fc\u30c9\u3055\u308c\u3001\u5358\u8a9e\u306e\u6700\u5c0f\u91cd\u91cf\u306f\u5c11\u306a\u304f\u3068\u308216\u3067\u3042\u308a\u30017\u30d3\u30c3\u30c8\u306e\u30a8\u30e9\u30fc\u88dc\u6b63\u3092\u53ef\u80fd\u306b\u3057\u307e\u3057\u305f\u3002\u3068\u3068\u3082\u306b 2 6 = \u516d\u5341\u56db {displaystyle 2^{6} = 64} \u30b3\u30fc\u30c9\u30ef\u30fc\u30c9\u306f\u3001\u30d4\u30af\u30bb\u30eb\u306e\u30b0\u30ec\u30fc\u5024\u3092\u30b3\u30fc\u30c9\u3057\u307e\u3057\u305f\u3002\u3053\u308c\u306b\u3064\u3044\u3066\u306f\u3001\u6b21\u306e\u4f8b3\u306eNASA RAUM PROBE MARINER 9\u3078\u306e\u8a73\u7d30\u3002 \u4ee5\u4e0b\u306f\u3001\u9577\u3055\u306e\u30ea\u30fc\u30c9\u30df\u30e5\u30e9\u30fc\u30b3\u30fc\u30c9\u306e\u30d7\u30ed\u30c7\u30e5\u30fc\u30b5\u30fc\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u4f5c\u6210\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4n = 2 d {displaystyle n = 2^{d}} \u69cb\u7bc9\u3055\u308c\u3066\u3044\u307e\u3059 \u30d0\u30c4 = F2d= { \u30d0\u30c4 1\u3001 &#8230; \u3001 \u30d0\u30c4 2d} {displaystyle x = mathbb {f} _ {2}^{d} = {x_ {1}\u3001ldots\u3001x_ {2^{d}}}}} \u3002 f n {displaystyle mathbb {f} _ {n}} \u975e\u9670\u6027\u6570\u306e\u30b5\u30d6\u30bb\u30c3\u30c8\u3067\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Fn= { a \u2208 N0| a < n } {displaystyle mathbb {f} _ {n} = {ain mathbb {n} _ {0}; |; \u3002 N\u6b21\u5143\u7a7a\u9593\u3067\u5b9a\u7fa9\u3057\u307e\u3059 f 2 n {displaystyle mathbb {f} _ {2}^{n}} \u30a4\u30f3\u30b8\u30b1\u30fc\u30bf\u30d9\u30af\u30c8\u30eb\uff1a IA\u2208 F2n{displaystyle mathbb {i} _ {a} in mathbb {f} _ {2}^{n}} \u6df7\u5408\u7269 a \u2282 \u30d0\u30c4 {displaystyle asubset x} \u7d42\u3048\u305f\uff1a (IA)i= {1\u00a0wenn\u00a0xi\u2208A0\u00a0sonst{displaystyle left\uff08mathbb {i} _ {a} right\uff09_ {i} = {begin {cases} 1\uff06{mbox} {wenn}} x_ {i} in {mbox {sonst}} \\ \\ end {case}}}}}} \u305d\u3057\u3066 &#8211; \u307e\u305f f 2 n {displaystyle mathbb {f} _ {2}^{n}}  &#8211; \u30d0\u30a4\u30ca\u30ea\u64cd\u4f5c\uff1a \u306e \u2227 \u3068 = \uff08 \u306e 1\u00d7 \u3068 1\u3001 &#8230; \u3001 \u306e n\u00d7 \u3068 n\uff09\uff09 {displaystyle wwedge z =\uff08w_ {1} times z_ {1}\u3001ldots\u3001w_ {n} times z_ {n}\uff09} \u3068\u3057\u3066 \u30a6\u30a7\u30c3\u30b8\u88fd\u54c1 \u3068\u547c\u3070\u308c\u307e\u3059\u3002 f 2 d {displaystyle mathbb {f} _ {2}^{d}} a\u3067\u3059 d {displaystyle d}  &#8211; \u6b21\u5143\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3092\u8d85\u3048\u307e\u3059 f 2 {displaystyle mathbb {f} _ {2}} \u3001\u3057\u305f\u304c\u3063\u3066\u3001\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff1a \uff08 f 2 \uff09\uff09 d = { \uff08 \u3068 \u521d\u3081 \u3001 &#8230; \u3001 \u3068 d \uff09\uff09 | \u3068 \u79c1 \u2208 f 2 } {displaystyle\uff08mathbb {f} _ {2}\uff09^{d} = {\uff08y_ {1}\u3001ldots\u3001y_ {d}\uff09; |; y_ {i} in mathbb {f} _ {2}}}}  \u3067\u5b9a\u7fa9\u3057\u307e\u3059 n {displaystyle n}  &#8211; \u6b21\u5143\u7a7a\u9593 f 2 n {displaystyle mathbb {f} _ {2}^{n}} \u9577\u3055\u306e\u6b21\u306e\u30d9\u30af\u30c8\u30eb n {displaystyle n}  \u306e 0 = \uff08 \u521d\u3081 \u3001 \u521d\u3081 \u3001 &#8230; \u3001 \u521d\u3081 \uff09\uff09 {displaystyle v_ {0} =\uff081,1\u3001ldots\u30011\uff09} \u3068 \u306e i= IHi{displaystyle v_ {i} = mathbb {i} _ {h_ {i}}}}} \u3001 \u3057\u305f\u304c\u3063\u3066 h \u79c1 {displaystyle h_ {i}} \u30cf\u30a4\u30d1\u30fc\u30ec\u30d9\u30eb \uff08 f 2 \uff09\uff09 d {displaystyle\uff08mathbb {f} _ {2}\uff09^{d}} \uff08\u5bf8\u6cd5\u4ed8\u304d d  &#8211;  \u521d\u3081 {displaystyle d-1} \uff09 \u305d\u308c\u306f\uff1a h i= { \u3068 \u2208 \uff08 F2\uff09\uff09 d&#8216; \u3068 i= 0 } {displaystyle h_ {i} = {yin\uff08mathbb {f} _ {2}\uff09^{d} mid y_ {i} = 0}}}  Reed-Muller RM\uff08D\u3001R\uff09-Code \u6ce8\u6587 r {displaystyle r} \u305d\u3057\u3066\u9577\u3055 n = 2 d {displaystyle n = 2^{d}} \u30b9\u30eb\u30fc\u306e\u30b3\u30fc\u30c9\u3067\u3059 \u306e 0 {displaystyle v_ {0}} \u305d\u3057\u3066\u3001\u30a6\u30a7\u30c3\u30b8\u88fd\u54c1\u304b\u3089 r {displaystyle r}  \u306e \u79c1 {displaystyle v_ {i}} \u751f\u6210\u3055\u308c\u307e\u3059\uff081\u3064\u672a\u6e80\u306e\u30d9\u30af\u30c8\u30eb\u306e\u30a6\u30a7\u30c3\u30b8\u7a4d\u304c\u3053\u306e\u6f14\u7b97\u5b50\u306eID\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\uff09\u3002 \u6b21\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u304c\u9069\u7528\u3055\u308c\u307e\u3059 \u53ef\u80fd\u306a\u3059\u3079\u3066\u306e\u30a6\u30a7\u30c3\u30b8\u88fd\u54c1\u306e\u91cf\u304b\u3089 d  \u306e i{displaystyle v_ {i}} \u306e\u57fa\u790e\u3092\u5f62\u6210\u3057\u307e\u3059 F2n{displaystyle mathbb {f} _ {2}^{n}} \u3002 RM\uff08D\u3001R\uff09\u30b3\u30fc\u30c9\u306b\u306f\u30e9\u30f3\u30af\u304c\u3042\u308a\u307e\u3059\u3002 \u2211 s=0r(ds){displaystyle sum _ {s = 0}^{r} {d choice s}} \u9069\u7528\u3055\u308c\u307e\u3059 r m \uff08 d \u3001 r \uff09\uff09 = r m \uff08 d  &#8211;  \u521d\u3081 \u3001 r \uff09\uff09 | r m \uff08 d  &#8211;  \u521d\u3081 \u3001 r  &#8211;  \u521d\u3081 \uff09\uff09 {displaystyle rm\uff08d\u3001r\uff09= rm\uff08d-1\u3001r\uff09| rm\uff08d-1\u3001r-1\uff09} \u3001\u305d\u308c\u306b\u3088\u3063\u3066 | {displaystyle |} 2\u3064\u306e\u30b3\u30fc\u30c9\u306e\u30d0\u30fc\u751f\u7523\u306f\u793a\u3055\u308c\u307e\u3059 rm\uff08d\u3001r\uff09\u306f\u6700\u5c0f\u9650\u306e\u30cf\u30df\u30f3\u30b0\u8ddd\u96e2\u3092\u6301\u3063\u3066\u3044\u307e\u3059 2 d\u2212r{displaystyle 2^{d-r}} \u3002 \u591a\u5206 d = 3 {displaystyle d = 3} \u3002\u305d\u308c\u304b\u3089 n = 8 {displaystyle n = 8} \u3001 \u3068 \u30d0\u30c4 = F23= { \uff08 0 \u3001 0 \u3001 0 \uff09\uff09 \u3001 \uff08 0 \u3001 0 \u3001 \u521d\u3081 \uff09\uff09 \u3001 &#8230; \u3001 \uff08 \u521d\u3081 \u3001 \u521d\u3081 \u3001 \u521d\u3081 \uff09\uff09 } \u3002 {displaystyle x = mathbb {f} _ {2}^{3} = {\uff080,0,0\uff09\u3001\uff080,0,1\uff09\u3001ldots\u3001\uff081,1,1\uff09}\u3002}} \u3068 v0=(1,1,1,1,1,1,1,1)v1=(1,0,1,0,1,0,1,0)v2=(1,1,0,0,1,1,0,0)v3=(1,1,1,1,0,0,0,0){displaystyle {begin {matrix} v_ {0}\uff06=\uff06\uff081,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0\uff09 \u30010,0,0\uff09\\ end {matrix}}} RM\uff083.1\uff09\u30b3\u30fc\u30c9\u306f\u6570\u91cf\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u307e\u3059 { \u306e 0\u3001 \u306e 1\u3001 \u306e 2\u3001 \u306e 3} {displaystyle {v_ {0}\u3001v_ {1}\u3001v_ {2}\u3001v_ {3}}}}}}}}} \u3088\u308a\u6b63\u78ba\u306b\u306f\u3001\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u7dda\u3092\u4ecb\u3057\u3066 (11111111101010101100110011110000){displaystyle {begin {pmatrix} 1\uff061\uff061\uff061\uff061\uff061\uff061\uff061\uff061\uff061\uff061\uff061 \\ 1\uff060\uff061\uff060\uff061\uff060\uff061\uff060 \\ 1\uff061\uff061\uff060\uff061\uff061\uff061\uff060\uff060 \\ 1\uff061\uff061\uff061\uff061\uff060\uff060\uff060\uff060 \\ end {pmatrix}}}}}} RM\uff083.2\uff09\u30b3\u30fc\u30c9\u306f\u6570\u91cf\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u307e\u3059 { \u306e 0\u3001 \u306e 1\u3001 \u306e 2\u3001 \u306e 3\u3001 \u306e 1\u2227 \u306e 2\u3001 \u306e 1\u2227 \u306e 3\u3001 \u306e 2\u2227 \u306e 3} {displaystyle {v_ {0}\u3001v_ {1}\u3001v_ {2}\u3001v_ {3}\u3001v_ {1}\u30a6\u30a7\u30c3\u30b8V_ {2}\u3001v_ {1}\u30a6\u30a7\u30c3\u30b8V_ {3}\u3001V_ {2}\u30a6\u30a7\u30c3\u30b8V_ {3}}}}}}} \u3088\u308a\u6b63\u78ba\u306b\u306f\u3001\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u7dda\u3092\u4ecb\u3057\u3066 (11111111101010101100110011110000100010001010000011000000){displaystyle {begin{pmatrix}1&#038;1&#038;1&#038;1&#038;1&#038;1&#038;1&#038;1\\1&#038;0&#038;1&#038;0&#038;1&#038;0&#038;1&#038;0\\1&#038;1&#038;0&#038;0&#038;1&#038;1&#038;0&#038;0\\1&#038;1&#038;1&#038;1&#038;0&#038;0&#038;0&#038;0\\1&#038;0&#038;0&#038;0&#038;1&#038;0&#038;0&#038;0\\1&#038;0&#038;1&#038;0&#038;0&#038;0&#038;0&#038;0\\1&#038;1&#038;0&#038;0&#038;0&#038;0&#038;0&#038;0\\end{pmatrix}}} \u30b3\u30f3\u30c8\u30ed\u30fc\u30eb\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u4e0d\u8db3\u3092\u4f34\u3046\u30ea\u30fc\u30c9\u30df\u30e5\u30e9\u30fc\u30b3\u30fc\u30c9\uff081\u30015\uff09\u306f\u30011971\u5e74\u306eNASA\u30e9\u30a6\u30e1\u30f3\u30d7\u30ed\u30fc\u30d6\u30de\u30ea\u30ca\u30fc9\u3067\u4f7f\u7528\u3055\u308c\u307e\u3057\u305f\u3002\u3053\u308c\u306f\u3001\u4e00\u822c\u7684\u306a\u30ea\u30fc\u30c9\u30df\u30e5\u30e9\u30fc\u30b3\u30fc\u30c9\u306e\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u30b3\u30fc\u30c9\u306f\u3001\u6700\u7d42\u7684\u306b\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3092\u5099\u3048\u305fHadamard\u30b3\u30fc\u30c9\u3067\u3057\u305f\uff0832\u30016\u300116\uff09\u3002\u3053\u306eRM\u30b3\u30fc\u30c9\uff0832\u30016\u300116\uff09\u3067\u306f\u300132\u30d3\u30c3\u30c8\u306e\u9577\u3044\u30b3\u30fc\u30c9\u30ef\u30fc\u30c9\u304c\u8ee2\u9001\u3055\u308c\u307e\u3057\u305f 2 6 = \u516d\u5341\u56db {displaystyle 2^{6} = 64} \u30b3\u30fc\u30c9\u5316\u3055\u308c\u305f\u5024\u3067\u306f\u3001\u4e92\u3044\u306b\u30b3\u30fc\u30c9\u30ef\u30fc\u30c9\u306e\u30d8\u30df\u30f3\u30b0\u8ddd\u96e2\u306f16\u3067\u3057\u305f\u3002\u3053\u308c\u3089\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306f\u3001\u30c1\u30e3\u30cd\u30eb\u306e\u7279\u6027\u3001\u753b\u50cf\u89e3\u50cf\u5ea6\u3001\u8a18\u9332\u3068\u9001\u4fe1\u6642\u9593\u306e\u305f\u3081\u306b\u9078\u629e\u3055\u308c\u3001\u8c4a\u5bcc\u306a30\u30d3\u30c3\u30c8\u306e\u5358\u8a9e\u306e\u9577\u3055\u3092\u610f\u5473\u3057\u307e\u3057\u305f\u3002 \u706b\u661f\u3068\u5730\u7403\u306e\u9593\u306e\u8ddd\u96e2\u304c\u9577\u3044\u305f\u3081\u3001\u305d\u3057\u3066\u4eca\u65e5\u3068\u6bd4\u8f03\u3057\u3066\u540c\u3058\u6642\u671f\u306bUNFR\u30b9\u30c6\u30c3\u30d7\u3067\u3042\u3063\u305f\u8ee2\u9001\u88c5\u7f6e\u306e\u305f\u3081\u3001\u60f3\u5b9a\u3055\u308c\u308b\u8aa4\u5dee\u78ba\u7387\u306f5\uff05\u3067\u3057\u305f\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u8ffd\u52a0\u306e\u30a8\u30e9\u30fc\u88dc\u6b63\u30e1\u30ab\u30cb\u30ba\u30e0\u306a\u3057\u30676\u30d3\u30c3\u30c8\u3067\u30b0\u30ec\u30fc\u5024\u304c\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u3055\u308c\u305f\u305f\u3081\u300126\uff05\u306e\u7070\u8272\u306e\u5024\u78ba\u7387\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u8ee2\u9001\u3055\u308c\u305f\u5199\u771f\u306e\u7d044\u5206\u306e1\u304c\u53d7\u4fe1\u8005\u3068\u8aa4\u3063\u3066\u5230\u7740\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002 RM\u30b3\u30fc\u30c9\uff0832\u30016\u300116\uff09\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u540c\u3058\u30d3\u30c3\u30c85\uff05\u3067\u7070\u8272\u306e\u5024\u306e\u78ba\u7387\u30920.01\uff05\u306b\u6e1b\u3089\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u5de5\u4e8b [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ]  NASA\u30eb\u30fc\u30e0\u30d7\u30ed\u30fc\u30d6\u30de\u30ea\u30ca\u30fc9\uff081971\/1972\uff09\u306e\u30ea\u30fc\u30c9\u30df\u30e5\u30e9\u30fc\u30b3\u30fc\u30c9\uff081.5\uff09\u306e\u30cf\u30c0\u30de\u30fc\u30c9\u30b3\u30fc\u30c9\uff0832\u30016\u300116\uff09\u306e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3002\u30ab\u30e9\u30fc\u30d6\u30e9\u30c3\u30af\u306f\u30d0\u30a4\u30ca\u30ea\u6570\u5b571\u3092\u30a8\u30f3\u30b3\u30fc\u30c9\u3057\u3001\u8272\u306e\u767d\u306f\u30d0\u30a4\u30ca\u30ea\u68410\u3092\u30a8\u30f3\u30b3\u30fc\u30c9\u3057\u307e\u3059\u3002 \u4f7f\u7528\u3055\u308c\u308bRM\u30b3\u30fc\u30c9\uff0832\u30016\u300116\uff09\u306fHadamard\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059 h 32 {displaystyle h_ {32}} \u3002 \u306e\u5efa\u8a2d h 32 {displaystyle h_ {32}} Hadamard-Matrix\u304b\u3089\u306e\u518d\u5e30\u3092\u542b\u3080 h 1= (1){displaystyle h_ {1} = {begin {pmatrix} 1end {pmatrix}}}}} \u305d\u3057\u3066\u751f\u6210\u30eb\u30fc\u30eb h 2n= (HnHnHn\u2212Hn){displaystyle h_ {2n} = {begin {pmatrix} h_ {n}\uff06h_ {n} \\ h_ {n}\uff06-h_ {n} end {pmatrix}}}} Sylvester\u306b\u3088\u308b\u3068\u3001\u3053\u306e\u69cb\u9020\u306f\u3001SO -Called Walsh Matrizen\u3092\u4f5c\u6210\u3057\u307e\u3059 h 1= (1)\u3001 h 2= (111\u22121)\u3001 h 4= (11111\u221211\u2212111\u22121\u221211\u22121\u221211)\u3001 &#8230; {displaystyle h_ {1} = {begin {pmatrix} 1end {pmatrix}}\u3001h_ {2} = {begin {pmatrix} 1\uff061 \\ 1\uff06-1end {pmatrix}}\u3001h_ {4} = {pmatrix} 1\uff061\uff061 \\ 1\uff06-1\uff061\uff06-1 \\ 1\uff061\uff06-1\uff06-1\uff06-1 \\ 1\uff06-1\uff06-1\uff061END {pmatrix}}\u3001ldots} \u5b66\u4f4d\u304b\u3089\u6b63\u898f\u5316\u3055\u308c\u305fHadamard Matricer 2 k {displaystyle 2^{k}} \u4ee3\u8868\u3059\u308b\u3002 Hadamard Matrix\u304c\u3042\u308b\u5834\u5408 h 32 {displaystyle h_ {32}} \u5c11\u3057\u30d1\u30bf\u30fc\u30f3\u3068\u3057\u3066\u89e3\u91c8\u3055\u308c\u307e\u3059\uff08\u30d0\u30a4\u30ca\u30ea\u68411\u306e1\u3064\u30681\u3064\u30011\u3064\u306f1\u3064\u30011\u3064\u306f  &#8211;  \u521d\u3081 {displaystyle -1} \u30d0\u30a4\u30ca\u30ea\u6570\u5b570\uff09\u306e\u5834\u5408\u300132\u30d3\u30c3\u30c8\u306e\u9577\u3055\u306e32\u306e\u30b3\u30fc\u30c9\u30ef\u30fc\u30c9\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30b3\u30fc\u30c9\u30ef\u30fc\u30c9\u306e\u305d\u308c\u305e\u308c\u306f\u3001\u4ed6\u306e\u30b3\u30fc\u30c9\u30ef\u30fc\u30c9\u306b\u5bfe\u3057\u3066\u6570\u5b66\u8ddd\u96e2\u304c16\u307e\u305f\u306f32\u3067\u3059\u3002 Hadamard Matrix\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u306b\u3088\u308a h 32 {displaystyle h_ {32}} \u9006\u30cf\u30c0\u30de\u30fc\u30c9\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3067  &#8211;  h 32 {displaystyle -h_ {32}} 32\u30d3\u30c3\u30c8\u306e\u9577\u3055\u306e64\u500b\u306e\u30b3\u30fc\u30c9\u30ef\u30fc\u30c9\u3092\u53d6\u5f97\u3059\u308b\u3068\u3001\u5404\u30b3\u30fc\u30c9\u30ef\u30fc\u30c9\u306b\u306f\u4ed6\u306e\u30b3\u30fc\u30c9\u30ef\u30fc\u30c9\u306b\u5bfe\u3057\u3066\u30de\u30ec\u30c3\u30c8\u30ae\u30e3\u30c3\u30d7\u304c16\u306b\u306a\u308a\u307e\u3059\u3002\u306e\u3053\u306e\u7d44\u307f\u5408\u308f\u305b h 32 {displaystyle h_ {32}} \u3068  &#8211;  h 32 {displaystyle -h_ {32}} Hadamard\u30b3\u30fc\u30c9\u3092\u5b9a\u7fa9\u3057\u307e\u3059 2 6 = \u516d\u5341\u56db {displaystyle 2^{6} = 64} \u5024\u3092\u5024\u3067\u30b3\u30fc\u30c9\u3057\u307e\u3059 n {displaystyle n}  n {displaystyle n}  &#8211; \u30b3\u30fc\u30c9\u306e\u30c6\u30f3\u884c\u304c\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u96a3\u63a5\u3059\u308b\u56f3\u306f\u3001RMC\u306e\u5b8c\u5168\u306aHadamard\u30b3\u30fc\u30c9\uff0832\u30016\u300116\uff09\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u30d0\u30a4\u30ca\u30ea\u68411\u306e\u8272\u304c\u9ed2\u3001\u30d0\u30a4\u30ca\u30ea\u6841\u306e\u8272\u306f\u767d\u8272\u3067\u3059\u3002 Reed Muller\u30b3\u30fc\u30c9\u306e\u30af\u30e9\u30b9\u3082\u3001\u591a\u304f\u306e\u30a4\u30e9\u30b9\u30c8\u3067\u8b58\u5225\u3067\u304d\u307e\u3059\u3002\u91d1\u984d\u3092\u8003\u616e\u3057\u3066\u304f\u3060\u3055\u3044 \u306e = { f \u56f3 &#8216; f \uff1a F2m\u2192 F2} {displaystyle v = {f {text {illung}} mid fcolon mathbb {f} _ {2}^{m} righttarrow mathbb {f _ {2}}}}} \u3002 \u30a4\u30e9\u30b9\u30c8 f \u2208 \u306e {displaystyle fin v} \u3042\u306a\u305f\u3092\u901a\u3057\u3066\u884c\u308f\u308c\u307e\u3059 2 m{displaystyle {2^{m}}} \u6ce8\u6587\u304c\u77e5\u3089\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u753b\u50cf\u306f\u660e\u78ba\u306b\u6c7a\u5b9a\u3055\u308c\u307e\u3057\u305f\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3042\u306a\u305f\u306f\u3067\u304d\u307e\u3059 f {displaystyle f} \u307e\u305f\u3001\u95a2\u9023\u3059\u308b\u753b\u50cf\u30d9\u30af\u30c8\u30eb\u3092\u4ecb\u3057\u3066 \uff08 f \uff08 0 \uff09\uff09 \u3001 f \uff08 \u521d\u3081 \uff09\uff09 \u3001 &#8230; \u3001 f \uff08 2 m  &#8211;  \u521d\u3081 \uff09\uff09 \uff09\uff09 \u2208 f 2 2m{displaystyle\uff08f\uff080\uff09\u3001f\uff081\uff09\u3001dots\u3001f\uff082^{m} -1\uff09\uff09in mathbb {f} _ {2}^{2^{m}}} \u8b70\u8ad6\u3092\u8868\u3057\u307e\u3059 0 \u3001 \u521d\u3081 \u3001 &#8230; \u3001 2 m  &#8211;  \u521d\u3081 {displaystyle 0,1\u3001dots\u30012^{m} -1}  2 {displaystyle 2}  &#8211; \u5b9a\u7fa9\u7bc4\u56f2\u304b\u3089\u306e\u8981\u7d20\u306eadian\u958b\u767a f 2 m {displaystyle mathbb {f} _ {2}^{m}} \u305d\u308c\u306f\u3002\u306e\u4e0a \u306e {displaystyle v} \u7b97\u8853\u64cd\u4f5c\u306b\u5f93\u3063\u3066\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u306e\u8ffd\u52a0\u3068\u4e57\u7b97\u3067\u304d\u307e\u3059\u304b f 2 {displaystyle mathbb {f} _ {2}} \u5b9a\u7fa9\u3002\u53b3\u5bc6\u306b\u8a00\u3048\u3070\u3001\u753b\u50cf\u306e\u91cf\u306e\u9593\u306b\u30ea\u30f3\u30b0\u306e\u540c\u578b\u304c\u3042\u308a\u307e\u3059 \u306e {displaystyle v} \u753b\u50cf\u30d9\u30af\u30c8\u30eb\u306e\u91cf f 2 2m{displaystyle mathbb {f} _ {2}^{2^{m}}}}} \u3001\u305d\u308c\u304c\u3042\u306a\u305f\u306e\u753b\u50cf\u30d9\u30af\u30c8\u30eb\u3067\u30a4\u30e9\u30b9\u30c8\u3092\u8b58\u5225\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u7406\u7531\u3067\u3059\uff1a f = \uff08 f \uff08 0 \uff09\uff09 \u3001 f \uff08 \u521d\u3081 \uff09\uff09 \u3001 &#8230; \u3001 f \uff08 2 m  &#8211;  \u521d\u3081 \uff09\uff09 \uff09\uff09 {displaystyle f =\uff08f\uff080\uff09\u3001f\uff081\uff09\u3001dots\u3001f\uff082^{m} -1\uff09\uff09} \u3002\u306e \u306e {displaystyle v} \u7279\u5225\u306a\u30a4\u30e9\u30b9\u30c8\u3001SO -Caled Coordinate\u95a2\u6570\u3067\u3059 \u3068 \u79c1 \u3001 \u79c1 \u2208 { \u521d\u3081 &#8230; 2 m } {displaystyle z_ {i}\u3001; iin {1dots 2^{m}}}}} \u3002 \u3053\u308c\u3089\u306f\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059\u3002 \u3068 i\uff08 \u306e \uff09\uff09 \uff1a= \u306e i{displaystyle z_ {i}\uff08v\uff09\uff1a= v_ {i}} \u305f\u3081\u306b \u306e = \uff08 \u306e 1\u3001 &#8230; \u3001 \u306e m\uff09\uff09 \u2208 F2m{displaystyle v =\uff08v_ {1}\u3001dots\u3001v_ {m}\uff09in mathbb {f} _ {2}^{m}} \u3002 \u5ea7\u6a19\u95a2\u6570\u306f\u3001\u4e0a\u8a18\u3067\u7d39\u4ecb\u3057\u305fVectord\u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u306b\u3082\u8a18\u8ff0\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 \u3068 i= \uff08 0,\u2026,0\u23df2i\u22121-mal\u3001 1,\u2026,1\u23df2i\u22121-mal\u3001 0,\u2026,0\u23df2i\u22121-mal\u3001 &#8230; \uff09\uff09 \u2208 F22m{displaystyle z_ {i} =\uff08underbrace {0\u3001dots\u30010} _ {2^{i-1} {text {mal}}}\u3001underbrace {1\u3001dots\u30011} _ {2^{i-1} {pepties {-mal}}}}} {-mal}}}\u3001dots\uff09in mathbb {f} _ {2}^{2^{m}}}} \u3002 \u3053\u3053\u3067\u9069\u7528\u3055\u308c\u307e\u3059\uff1a \u30e2\u30ce\u30e1\u30f3\u306e\u30b7\u30b9\u30c6\u30e0 \u3068 i1de \u22ef de \u3068 ik{displaystyle z_ {i_ {1}} cdot dots cdot z_ {i_ {k}}}}} \uff08 \u521d\u3081 \u2264 \u79c1 1< \u22ef < \u79c1 k\u2264 m \u3001 k = 0 \u3001 &#8230; \u3001 m {displaystyle 1leq i_ {1} F2\u56f3 &#8216; \u5352\u696d\u751f \u2061 \uff08 f \uff09\uff09 \u2264 r } \u2286 \u306e {displayStyle {fcolon mathbb {f} _ {2}^{m} righttarrow mathbb {f} _ {2} {text {Illustration}} Mid Operatorname {Degrees}\uff08f\uff09leq r} subseeteq V}} Reed Muller Code RM\uff08R\u3001M\uff09\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u3053\u3053\u306f \u5352\u696d\u751f \u2061 \uff08 f \uff09\uff09 {displaystyle operatorname {grad}\uff08f\uff09} \u5408\u8a08\u3068\u3057\u3066\u3001\u6700\u3082\u9ad8\u3044\u30e2\u30ce\u30de\u30eb\u306e\u5ea7\u6a19\u95a2\u6570\u304c\u6a5f\u80fd\u3057\u307e\u3059 f {displaystyle f} 1\u306b\u5f93\u3063\u3066\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u30a2\u30a4\u30c7\u30a2\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002ReedMuller\u30b3\u30fc\u30c9\u306e\u3059\u3079\u3066\u306e\u30b3\u30fc\u30c9\u30ef\u30fc\u30c9rm\uff08r\u3001m\uff09\u306f\u3001\u4e0a\u8a18\u306e\u4ee3\u66ff\u306e\u7279\u6027\u8a55\u4fa1\u306b\u5f93\u3063\u3066\u6a5f\u80fd\u306b\u306a\u308a\u307e\u3059 f {displaystyle f} out \u306e {displaystyle v} \u7406\u89e3\u3055\u308c\u3066\u3044\u307e\u3059 &#8211; \u53cd\u5bfe\u306e\u5ea7\u6a19\u95a2\u6570\u306e\u57fa\u672c\u7684\u306a\u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u3067\u3001i\u3002 H.\u660e\u78ba\u306b\u6c7a\u5b9a\u3055\u308c\u305f\u4fc2\u6570\u3092\u4f7f\u7528\u3057\u307e\u3059 m \u79c1 \u3068 \u79c1 \u2286 m {displaystyle m_ {i} {text {mit}} isubseteq m} \u3057\u305f\u304c\u3063\u3066 m = { \u521d\u3081 \u3001 &#8230; \u3001 m } {displaystyle m = {1\u3001dots\u3001m}} \u5ea7\u6a19\u95a2\u6570\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u91cf\u3002\u95a2\u6570 f {displaystyle f} \u753b\u50cf\u30d9\u30af\u30c8\u30eb\u3068\u3057\u3066\u3067\u3059 \uff08 f \uff08 0 \uff09\uff09 \u3001 f \uff08 \u521d\u3081 \uff09\uff09 \u3001 &#8230; \u3001 f \uff08 2 m  &#8211;  \u521d\u3081 \uff09\uff09 \uff09\uff09 {displaystyle\uff08f\uff080\uff09\u3001f\uff081\uff09\u3001dots\u3001f\uff082^{m} -1\uff09\uff09} \u90aa\u9b54\u3055\u308c\u305f\u30c1\u30e3\u30cd\u30eb\u3092\u901a\u3057\u3066\u9001\u4fe1\u3055\u308c\u307e\u3059\u3002\u53d7\u4fe1\u8005\u306f\u3053\u308c\u3092\u30a8\u30e9\u30fc\u3067\u89e3\u8aad\u3057\u307e\u3059 \u305d\u3046\u3067\u3059 {displaystyle e} \u30b3\u30fc\u30c9\u30ef\u30fc\u30c9\u306e\u5897\u52a0 g = f + \u305d\u3046\u3067\u3059 {displaystyle g = f+e} \u5f90\u3005\u306b\u4fc2\u6570\u306b\u3088\u3063\u3066 m \u79c1 {displaystyle m_ {i}} \u518d\u69cb\u7bc9\u3055\u308c\u307e\u3057\u305f\u3002\u5f7c\u306f\u30e2\u30ce\u30e0\u3067\u6700\u9ad8\u306e\u7a0b\u5ea6\u306e\u4fc2\u6570\u304b\u3089\u59cb\u307e\u308a\u307e\u3059 r {displaystyle r} \u5c5e\u3059\u308b\u3002\u3053\u308c\u3092\u884c\u3046\u305f\u3081\u306b\u3001\u5f7c\u306f\u306e\u30b9\u30ab\u30e9\u30fc\u7a4d\u3092\u8a08\u7b97\u3057\u307e\u3059 g {displaystyle g} S.G.\u30e2\u30ce\u30e0\u306e\u7279\u5fb4\u7684\u306a\u6a5f\u80fd\u3002\u3053\u308c\u3089\u306f\u3059\u3079\u3066\u7a0b\u5ea6\u306e\u56f3\u3067\u3059 m  &#8211;  r {displaystyle M-r} \u3001\u751f\u6210\u5ea7\u6a19\u95a2\u6570\u3082\u767a\u751f\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u5927\u591a\u6570\u304c\u30b9\u30ab\u30e9\u30fc\u88fd\u54c1\u306b\u3088\u3063\u3066\u8a08\u7b97\u3055\u308c\u308b\u5024\u306f\u3001\u5143\u306e\u30e2\u30ce\u30e0\u4fc2\u6570\u3067\u3059\u3002\u624b\u9806\u306f\u3001\u5b66\u4f4d\u304b\u3089\u30e2\u30ce\u30e1\u30f3\u306b\u3042\u308a\u307e\u3059 r  &#8211;  \u521d\u3081 \u3001 r  &#8211;  2 \u3001 &#8230; \u3001 0 {displaystyle r-1\u3001r-2\u3001dots\u30010} \u7e70\u308a\u8fd4\u3055\u308c\u308b\u3068\u3001\u3064\u3044\u306b\u5f97\u3089\u308c\u307e\u3059 f {displaystyle f}  &#8211; \u30a8\u30e9\u30fc\u3092\u63d0\u4f9b\u3057\u307e\u3057\u305f \u305d\u3046\u3067\u3059 {displaystyle e} \u5927\u304d\u3059\u304e\u307e\u305b\u3093\u3002 \u30ea\u30fc\u30c9\u30df\u30e5\u30e9\u30fc\u30b3\u30fc\u30c9\u3092\u4f7f\u7528\u3057\u305f\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u304a\u3088\u3073\u30c7\u30b3\u30fc\u30c9\u30d7\u30ed\u30bb\u30b9\uff1a \u30cb\u30e5\u30fc\u30b9 n {displaystyle n} \u30b3\u30fc\u30c9\u30ef\u30fc\u30c9\u3067\u3059 c {displaystyle c} \u7ffb\u8a33\u3002 \u30b3\u30fc\u30c9\u30ef\u30fc\u30c8 c {displaystyle c} \u30a4\u30e9\u30b9\u30c8\u3067\u3067\u304d\u307e\u3059 f {displaystyle f} \u8b58\u5225\u3055\u308c\u307e\u3059\u3002 \u56f3 f {displaystyle f} \u307e\u305f\u3001\u753b\u50cf\u30d9\u30af\u30c8\u30eb\u306b\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059 \uff08 f \uff08 0 \uff09\uff09 \u3001 f \uff08 \u521d\u3081 \uff09\uff09 \u3001 &#8230; \u3001 f \uff08 2 m &#8211;  \u521d\u3081 \uff09\uff09 \uff09\uff09 {displaystyle\uff08f\uff080\uff09\u3001f\uff081\uff09\u3001dots\u3001f\uff082^{m} -1\uff09\uff09} \u8868\u73fe\u3055\u308c\u3066\u3044\u307e\u3059\u3002 \u306e\u30e2\u30ce\u30e0\u4fc2\u6570\u306e\u4ee3\u308f\u308a\u306b\u8ee2\u9001 f {displaystyle f} \u95a2\u9023\u3059\u308b\u753b\u50cf\u30d9\u30af\u30c8\u30eb\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u5197\u9577\u6027\u304c\u63d0\u4f9b\u3055\u308c\u3001\u76ee\u7684\u306e\u30a8\u30e9\u30fc\u4fee\u6b63\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002 \u4e71\u308c\u305f\u30c1\u30e3\u30cd\u30eb\u3092\u4ecb\u3057\u3066\u753b\u50cf\u30d9\u30af\u30c8\u30eb\u3092\u9001\u4fe1\u3057\u307e\u3059\u3002\u7d50\u679c\u3067\u3059 g = f + \u305d\u3046\u3067\u3059 {displaystyle g = f+e} \u30a8\u30e9\u30fc\u30d9\u30af\u30c8\u30eb\u4ed8\u304d \u305d\u3046\u3067\u3059 {displaystyle e} \u3002 \u753b\u50cf\u30d9\u30af\u30c8\u30eb\u3092\u53d7\u4fe1\u3057\u307e\u3059 g {displaystyle g} \u5ea7\u6a19\u95a2\u6570\u3092\u4f7f\u7528\u3057\u305f\u30b9\u30ab\u30e9\u30fc\u306e\u624d\u80fd\u3092\u901a\u3058\u3066\u5229\u76ca\u3092\u5f97\u308b \u3068 i{displaystyle z_ {i}} \u5143\u306e\u30e2\u30ce\u30e0\u4fc2\u6570\u3002 \u30e2\u30ce\u30e0\u4fc2\u6570\u306e\u305f\u3081\u3001\u5143\u306e\u56f3\/\u30b3\u30fc\u30c9\u30ef\u30fc\u30c9\u304c\u8a08\u7b97\u3055\u308c\u307e\u3059 f = c {displaystyle f = c} \u3057\u305f\u304c\u3063\u3066 n {displaystyle n} \u3002 \u30d7\u30ed\u30c3\u30c8\u30ad\u30f3\u69cb\u9020\u3092\u5099\u3048\u305f\u518d\u5e30\u30b3\u30fc\u30c9 \uff08PDF; 1.7 MB\uff09\u30ea\u30fc\u30c9\u30df\u30e5\u30e9\u30fc\u30b3\u30fc\u30c9\u3068\u305d\u306e\u30b5\u30d6\u30b3\u30fc\u30c9\u306e\u69cb\u7bc9\u3068\u30c7\u30b3\u30fc\u30c9\u306e\u305f\u3081\u306e\u8ad6\u6587\uff08\u6ce8\u610f\uff1a\u30de\u30ea\u30ca\u30fc9\u30df\u30c3\u30b7\u30e7\u30f3\u306eRM\u30b3\u30fc\u30c9\uff0832\u30016\u300116\uff09\u306e\u8868\u793a\u306f\u6b63\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002 2 5= 32 {displaystyle 2^{5} = 32} \u5024\u304c\u4e0e\u3048\u3089\u308c\u3001\u8aac\u660e\u3055\u308c\u3066\u3044\u307e\u3059\u3002\uff09      (adsbygoogle = window.adsbygoogle || 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