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Designs, Codes and Cryptography

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17-08-2023

BCH codes with larger dimensional hull

Authors: Binbin Pang, Shixin Zhu, Tian Yang, Jun Gao

Published in: Designs, Codes and Cryptography | Issue 12/2023

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Abstract

Hulls of linear codes are widely studied due to their good properties and wide applications. Let \(n=\frac{q^m-1}{r}\) and \(\mathcal {C}\) be an [n, k] cyclic code over \(\mathbb {F}_q\), where \(r|q-1\). In this paper, we present several necessary and sufficient conditions for BCH codes of length n that have \(k-1\) or \(k^\perp -1\) dimensional hulls, where \(k^\perp \) is the dimension of \(\mathcal {C}^\perp \). Further, we give the parameters of several families of self-orthogonal codes that arise as hulls of BCH codes. We obtain many optimal codes.

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Title: BCH codes with larger dimensional hull
Authors: Binbin Pang
Shixin Zhu
Tian Yang
Jun Gao
Publication date: 17-08-2023
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 12/2023
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-023-01281-x

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