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A new construction of linear codes with one-dimensional hull

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Abstract

The hull of a linear code C is the intersection of C with its dual \(C^\perp \). The hull with low dimensions gets much interest due to its crucial role in determining the complexity of algorithms for computing the automorphism group of a linear code and for checking permutation equivalence of two linear codes. The hull of linear codes has recently found its application to the so-called entanglement-assisted quantum error-correcting codes (EAQECCs). In this paper, we provide a new method to construct linear codes with one-dimensional hull. This construction method improves the code lengths and dimensions of the recent results given by the author. As a consequence, we derive several new classes of optimal linear codes with one-dimensional hull. Some new EAQECCs are presented.

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Acknowledgements

The author would like to thank the anonymous referees for their constructive comments which have improved the quality of the paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Anhui University, Hefei, 230601, Anhui, China

    Lin Sok

  2. Department of Mathematics, Royal University of Phnom Penh, Phnom Penh, 12156, Cambodia

    Lin Sok

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  1. Lin Sok
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Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This research work is supported by Anhui Provincial Natural Science Foundation with Grant Number 1908085MA04.

This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue: On Coding Theory and Combinatorics: In Memory of Vera Pless”.

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Sok, L. A new construction of linear codes with one-dimensional hull. Des. Codes Cryptogr. 90, 2823–2839 (2022). https://doi.org/10.1007/s10623-021-00991-4

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  • DOI: https://doi.org/10.1007/s10623-021-00991-4

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