Quantum MDS codes induced by the projective linear transformation

IF 1.3 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2026-03-01 Epub Date: 2025-12-01 DOI:10.1016/j.ffa.2025.102764

Fengwei Li, Yuting Liu, Ruiyuan Jiang

引用次数: 0

Abstract

Let

F_{q}

be the finite field with q elements, where q is a power of an odd prime p. In this paper, we provide a method to construct Hermitian self-orthogonal generalized Reed-Solomon (GRS) codes and extended GRS codes, which their support sets are roots of polynomials from affine and projective linear transformation over

F_{q^{2}}

. Moreover, we construct three classes of quantum maximum distance separable (MDS) codes with minimum distances

> \frac{q}{2} + 1

. Some of these quantum MDS codes have not been obtained before, and in some cases, have larger minimum distances and higher efficiency than the well-known quantum MDS codes.

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投影线性变换诱导的量子MDS码

设Fq是有q个元素的有限域，其中q是奇素数p的幂。本文给出了一种构造hermite自正交广义里德-所罗门码（GRS）和扩展GRS码的方法，它们的支持集是Fq2上仿射和射影线性变换的多项式的根。此外，我们构造了3类最小距离为>；q2+1的量子最大距离可分离码（MDS）。这些量子MDS码有些是以前没有得到过的，在某些情况下，比已知的量子MDS码具有更大的最小距离和更高的效率。

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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来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.