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On the weight distribution of binary linear codes (Corresp.)

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LetVbe a binary linear(n,k)-code defined by a check matrixHwith columnsh_{1}, cdots ,h_{n}, and leth(x) = 1ifx in {h_{1}, cdots , h_{n}, andh(x) = 0ifx in neq {h_{1}, cdots ,h_{n}}. A combinatorial argument relates the Walsh transform ofh(x)with the weight distributionA(i)of the codeVfor smalli(i< 7). This leads to another proof of the Plessith power moment identities fori < 7. This relation also provides a simple method for computing the weight distributionA(i)for smalli. The implementation of this method requires at most(n-k+ 1)2^{n-k}additions and subtractions,5.2^{n-k}multiplications, and2^{n-k}memory cells. The method may be very effective if there is an analytic expression for the characteristic Boolean functionh(x). This situation will be illustrated by several examples.

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Information Theory, IEEE Transactions on  (Volume:25 ,  Issue: 1 )