DocumentCode :
929699
Title :
On the weight distribution of binary linear codes (Corresp.)
Author :
Karpovsky, Mark G.
Volume :
25
Issue :
1
fYear :
1979
fDate :
1/1/1979 12:00:00 AM
Firstpage :
105
Lastpage :
109
Abstract :
Let V be a binary linear (n,k) -code defined by a check matrix H with columns h_{1}, \\cdots ,h_{n} , and let h(x) = 1 if x \\in \\{h_{1}, \\cdots , h_{n}\\} , and h(x) = 0 if x \\in \\neq {h_{1}, \\cdots ,h_{n}} . A combinatorial argument relates the Walsh transform of h(x) with the weight distribution A(i) of the code V for small i(i< 7) . This leads to another proof of the Pless i th power moment identities for i < 7 . This relation also provides a simple method for computing the weight distribution A(i) for small i . The implementation of this method requires at most (n-k+ 1)2^{n-k} additions and subtractions, 5 . 2^{n-k} multiplications, and 2^{n-k} memory cells. The method may be very effective if there is an analytic expression for the characteristic Boolean function h(x) . This situation will be illustrated by several examples.
Keywords :
Linear codes; Walsh transforms; Block codes; Circuits; Computer science; Convolutional codes; Decoding; Fourier transforms; Linear code; Notice of Violation; Viterbi algorithm; Welding;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1979.1056001
Filename :
1056001
Link To Document :
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