【摘 要】
：
设Fq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X2m+1在Fq2[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Fq上长为2mpn的负循环自对偶码和自正交码的生成多项式(其形式为Fq上X2mpn+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 Fq be a
【机 构】
：
洛阳师范学院商学院,洛阳,河南,471934
论文部分内容阅读
设Fq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X2m+1在Fq2[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Fq上长为2mpn的负循环自对偶码和自正交码的生成多项式(其形式为Fq上X2mpn+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 Fq be a finite field with q elements.Let m be a positive integer such that X2m+1 factors completely into degree one factors over Fq2[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 2mpn over Fq in terms of the factorization of X2mpn+1 over Fq,where p is an odd prime relatively prime to q and n is a positive integer.
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