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Some results on the weight distribution of linear codes

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1 Author(s)

By studying the algebraic structure of the parity check matrix of a linear code we show that the weight distribution is a function only of the quantities N_{\upsilon }^{u} , the number of \upsilon columns of the parity check matrix with rank u . We apply this to obtain a new formula for the weight distribution of the distance 3 s -ary Hamming code and for the distance 4 s -ary conic code. We give the definition of a conic code and some of its properties.

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Information Theory, IEEE Transactions on  (Volume:15 ,  Issue: 6 )