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arXiv:2211.11147

Optimal quaternary linear codes with one-dimensional Hermitian hull and the related EAQECCs

Shitao Li, Minjia Shi, Huizhou Liu

Published Nov 21, 2022• 0 citations
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Abstract

Linear codes with small hulls over finite fields have been extensively studied due to their practical applications in computational complexity and information protection. In this paper, we develop a general method to determine the exact value of $D_4^H(n,k,1)$ for $n\leq 12$ or $k\in \{1,2,3,n-1,n-2,n-3\}$, where $D_4^H(n,k,1)$ denotes the largest minimum distance among all quaternary linear $[n,k]$ codes with one-dimensional Hermitian hull. As a consequence, we solve a conjecture proposed by Mankean and Jitman on the largest minimum distance of a quaternary linear code with one-dimensional Hermitian hull. As an application, we construct some binary entanglement-assisted quantum error-correcting codes (EAQECCs) from quaternary linear codes with one-dimensional Hermitian hull. Some of these EAQECCs are optimal codes, and some of them are better than previously known ones.

DOI
10.48550/arxiv.2211.11147

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