论文标题
具有一维遗传船体和相关的EAQECC的最佳第四纪线性代码
Optimal quaternary linear codes with one-dimensional Hermitian hull and the related EAQECCs
论文作者
论文摘要
由于其在计算复杂性和信息保护中的实际应用，因此对有限磁场上的小船体的线性代码进行了广泛的研究。 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。结果，我们解决了曼肯和吉特曼提出的一个猜想，该猜想是用一维遗传学船体的第四纪线性代码中最大的最小距离。作为一种应用，我们从第四纪线性代码中构建了一些具有一维遗传学船体的二进制纠缠量误差校正代码（EAQECC）。其中一些EAQECC是最佳代码，其中一些是比以前已知的更好的代码。
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.
