A new family of AMDS symbol-pair constacyclic codes of length $$\textbf{4p}$$ and symbol-pair distance $$\textbf{9}$$

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Designs, Codes and Cryptography Pub Date : 2025-02-27 DOI:10.1007/s10623-025-01600-4

Hai Q. Dinh, Hieu V. Ha, Bac T. Nguyen, Thieu N. Vo

引用次数: 0

Abstract

Let p be any prime number such that $p\equiv 1 \pmod 4$, and let ${\mathbb {F}}_p$ be the finite field of p elements. In this paper, we first construct a new AMDS symbol-pair cyclic code of length 4p and of symbol-pair distance 9 by examining its generator polynomial. We then use the generator polynomial to obtain a family of $(p-1)/2$ AMDS symbol-pair constacyclic codes of the same length and of the same symbol-pair distance.

查看原文本刊更多论文

一个新的AMDS符号对恒环码族，其长度为$$\textbf{4p}$$，符号对距离为0 $$\textbf{9}$$

设p为任意质数，满足$p\equiv 1 \pmod 4$，设${\mathbb {F}}_p$为p元素的有限域。本文首先通过检验其产生多项式，构造了一个长度为4p、符号对距离为9的AMDS符号对循环码。然后，我们使用生成多项式得到了具有相同长度和相同符号对距离的$(p-1)/2$ AMDS符号对恒环码族。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Designs, Codes and Cryptography 工程技术-计算机：理论方法

CiteScore

2.80

自引率

12.50%

发文量

157

审稿时长

16.5 months

期刊介绍： Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.