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MacWilliams identities : ウィキペディア英語版
Enumerator polynomial
In coding theory, the weight enumerator polynomial of a binary linear code specifies the number of words of each possible Hamming weight.
Let C \subset \mathbb_2^n be a binary linear code length n. The weight distribution is the sequence of numbers
: A_t = \#\
giving the number of codewords ''c'' in ''C'' having weight ''t'' as ''t'' ranges from 0 to ''n''. The weight enumerator is the bivariate polynomial
: W(C;x,y) = \sum_^n A_w x^w y^.
==Basic properties==
# W(C;0,1) = A_=1
# W(C;1,1) = \sum_^A_=|C|
# W(C;1,0) = A_= 1 \mbox (1,\ldots,1)\in C\ \mbox 0 \mbox
# W(C;1,-1) = \sum_^A_(-1)^ = A_+(-1)^A_+\ldots+(-1)^A_+(-1)^A_

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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