期刊论文

Pan, Xu

英文

DESIGNS CODES AND CRYPTOGRAPHY

0925-1022

2020

88

2

241-255

10.1007/s10623-019-00681-2

The authors sincerely thank Professor Jay A. Wood for valuable comments during his visit at Central China Normal University from April to May in 2018. We also thank the anonymous reviewers and the editor for their very helpful comments and suggestions, which have greatly improved the presentation of this paper. This work was supported by NSFC (Grant No. 11871025) and the self-determined research funds of CCNU from the colleges’ basic research and operation of MOE (Grant No. CCNU18TS028). Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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The $$\ell $$-Galois hull $$h_{\ell }(C)$$ of an [n, k] linear code C over the finite field $${\mathbb {F}}_q$$ is the intersection of C and $$C^{{\bot }_{\ell }}$$, where $$C^{\bot _{\ell }}$$ denotes the $$\ell $$-Galois dual of C which was introduced by Fan and Zhang in 2017. The $$\ell $$-Galois LCD code is a linear code C satisfying $$h_{\ell }(C)= C\bigcap C^{\bot _{\ell }}= \{0\}$$. In this paper, we show that the dimension of the $$\ell $$-Galois hull of a linear code is invariant under permutation equivalences and we provide a method to calculate the dimension of the $$\ell $$-Galois ...