有限域上长为2^(m)p^(n)的负循环自对偶码和自正交码  

Self-dual and Self-orthogonal Negacyclic Codes of Length 2^(m)p^(n) over Finite Fields

作　　者：梁淑华[1] LIANG Shuhua(School of Business,Luoyang Normal University,Luoyang,Henan,471934,P.R.China)

机构地区：[1]洛阳师范学院商学院,河南洛阳471934

出　　处：《数学进展》2021年第6期940-952,共13页Advances in Mathematics（China）

基　　金：Supported in part by the Science and Technology Development Program of Henan Province(No.192102310444);in part by the Key Research Project of Higher Education of the Education Department of Henan Province(No.19A120010)。

摘　　要：设F_(q)是一个q元有限域,q是一个奇素数幂.设m是一个正整数,使得X^(2m)+1在F_(q2)[X]上可完全分解成一次因式的乘积.受近期文献[IEEE Access,2019,7:121874-121880]对有限域上负循环码代数结构研究的启发,本文确定了有限域F_(q)上长为2^(m)p^(n)的负循环自对偶码和自正交码的生成多项式(其形式为F_(q)上X^(2mpn)+1的因式分解),给出了它们的计数公式,这里p是一个与q互素的奇素数,n是一个正整数.Let q be an odd prime power and let F_(q) be a finite field with q elements.Let m be a positive integer such that X^(2m)+1 factors completely into degree one factors over F_(q2)[X]·In this paper,motivated by the recent work[IEEE Access,2019,7:121874-121880]which considered the algebraic structure of negacyclic codes over finite fields,we determine the generator polynomials and give enumerative formulas for all self-dual and self-orthogonal negacyclic codes of length 2^(m)p^(n) over F_(q) in terms of the factorization of X^(2mpn)+1 over F_(q),where p is an odd prime relatively prime to q and n is a positive integer.

关 键 词：负循环码 生成多项式 自对偶码 自正交码 

分 类 号：O157.4[理学—数学]