Dimensions of some LCD BCH codes

05/11/2023

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by   Hanglong Zhang, et al.

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In this paper, we investigate the first few largest coset leaders modulo q^m+1/λ where λ| q+1 and q is an odd prime power, and give the dimensions of some LCD BCH codes of length q^m+1/λ with large designed distances.We also determine the dimensions of some LCD BCH codes of length n=(q^m+1)/λ with designed distances 2≤δ≤ q^⌊(m+1)/2⌋/λ+1, where λ| q+1 and 1<λ<q+1. The LCD BCH codes presented in this paper have a sharper lower bound on the minimum distance than the BCH bound.