Bounds for the weight distribution of weakly self-dual codes

DOI10.1109/18.904542zbMATH Open1019.94035arXivmath/0104016OpenAlexW2162012520MaRDI QIDQ4544482

Farrokh Vatan, Vwani Roychowdhury

Publication date: 4 August 2002

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/math/0104016

zbMATH Keywords

upper boundsHilbert spaceweight distributionquantum computingunitary operationsbinary weakly self-dual codes

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Quantum computation (81P68) Bounds on codes (94B65)

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