电子学报 ›› 2017, Vol. 45 ›› Issue (6): 1469-1474.DOI: 10.3969/j.issn.0372-2112.2017.06.027

• 学术论文 • 上一篇    下一篇

F4m上厄米特自正交常循环码

管乾清1, 开晓山1,2, 朱士信1,2   

  1. 1. 合肥工业大学数学学院, 安徽合肥 230009;
    2. 东南大学移动通信国家重点实验室, 江苏南京 210096
  • 收稿日期:2015-12-04 修回日期:2016-11-17 出版日期:2017-06-25
    • 通讯作者:
    • 管乾清
    • 作者简介:
    • 开晓山 男,1975年生,安徽青阳人,合肥工业大学数学学院副教授,硕士生导师,研究方向为编码理论与信息安全.E-mail:xskai@hfut.edu.cn
    • 基金资助:
    • 国家自然科学基金 (No.61370089,No.61572168); 安徽省自然科学基金 (No.JZ2015AKZR0229,No.1508085MA13,No.1408085QF116); 2014年安徽省高校优秀青年支持计划; 东南大学移动通信国家重点实验室开放研究基金 (No.2014D04)

Hermitian Self-Orthogonal Constacyclic Codes over F4m

GUAN Qian-qing1, KAI Xiao-shan1,2, ZHU Shi-xin1,2   

  1. 1. School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, China;
    2. National Mobile Communications Research Laboratory, Southeast University, Nanjing, Jiangsu 210096, China
  • Received:2015-12-04 Revised:2016-11-17 Online:2017-06-25 Published:2017-06-25

摘要:

有限域上常循环码具有丰富的代数结构,其编译码电路容易实现,因而在信息传输实践中具有重要的应用.该文研究了一类有限域上任意长度的厄米特自正交常循环码的结构,给出了此类有限域上厄米特自正交常循环码的生成多项式与存在条件,确立了此类有限域上厄米特自正交常循环码的计数公式,并且利用此类有限域上偶长度的厄米特自正交常循环码构造了最优的量子码.

关键词: 常循环码, 厄米特自正交码, 生成多项式, 量子码

Abstract:

Constacyclic codes over finite fields are a class of important linear codes.This class of codes has rich algebra structure and its encoding and decoding circuits can be easily performed.Constacyclic codes over finite fields have many applications in information transmission.In this paper,the structure of Hermitian self-orthogonal constacyclic codes over a class of finite fields of any length is studied.By using generator polynomial,the condition for the existence of Hermitian self-orthogonal constacyclic codes over this class of finite fields is explored and the enumeration formula of such codes is determined.Further,Hermitian self-orthogonal constacyclic codes over this class finite fields are applied to construct some optimal quantum codes.

Key words: constacyclic code, Hermitian self-orthogonal code, generator polynomial, quantum code

中图分类号: