Bounds for weight distribution of weakly self-dual codes

Details Bounds for weight distribution of weakly self-dual codes Bounds for weight distribution of weakly self-dual codes

2001-04-02

arxiv.org/abs/math/0104016v1

IEEE Transactions on Information Theory, vol. 47, no. 1, Jan. 2001, pp. 393-396

Mathematics

Combinatorics

9 pages

Scientific paper

Upper bounds are given for the weight distribution of binary weakly self-dual codes. To get these new bounds, we introduce a novel method of utilizing unitary operations on Hilbert spaces. This method is motivated by recent progress on quantum computing. This new approach leads to much simpler proofs for such genre of bounds on the weight distributions of certain classes of codes. Moreover, in some cases, our bounds are improvements on the earlier bounds. These improvements are achieved, either by extending the range of the weights over which the bounds apply, or by extending the class of codes subjected to these bounds.

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