构建 AEAQEC 代码的新方法

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-08-12 DOI:10.1016/j.disc.2024.114202

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引用次数: 0

摘要

最近，Liu 和 Liu给出了纯非对称纠缠辅助量子纠错（AEAQEC）码的辛格尔顿约束。他们通过范德蒙德矩阵、广义里德-所罗门（GRS）码和循环码构建了三个新的 AQEAEC 码族。在本文中，我们首先展示了任何 AEAQEC 码的辛格尔顿约束。然后，我们用两种不同的常循环码构造 AEAQEC 码。通过重复根循环码，我们构建了新的 AEAQEC MDS 码。此外，我们的方法还能轻松计算 AEAQEC 代码的维数、dz、dx 和预共享最大纠缠态的数量 c。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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New methods for constructing AEAQEC codes

Recently, Liu and Liu gave the Singleton bound for pure asymmetric entanglement-assisted quantum error-correcting (AEAQEC) codes. They constructed three new families of AQEAEC codes by means of Vandermonde matrices, generalized Reed-Solomon (GRS) codes and cyclic codes. In this paper, we first exhibit the Singleton bound for any AEAQEC codes. Then we construct AEAQEC codes by two distinct constacyclic codes. By means of repeated-root cyclic codes, we construct new AEAQEC MDS codes. In addition, our methods allow for easily calculating the dimensions, $d_{z}$ , $d_{x}$ and the number c of pre-shared maximally entangled states of AEAQEC codes.

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.