自共轭互反多项式的推广  

Generalizations of Self-Conjugate-Reciprocal Polynomials

作　　者：胡建 曹喜望[1] HU Jian;CAO Xiwang(College of Science,Nanjing University of Aeronautics and Astronautics,Nanjing 211106)

机构地区：[1]南京航空航天大学理学院,南京211106

出　　处：《系统科学与数学》2020年第8期1507-1516,共10页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11771007,61572027)资助课题。

摘　　要：文章给出有限域Fq2上xqn+1-λ的分解和首一不可约λ-自共轭互反多项式的计数公式,其中q是素数方幂,λ∈Fq*.进一步,得到了Fq2上xn+1的自共轭互反多项式因子的计数公式.将此公式应用在负循环码上,Fq2上厄米特互补对偶负循环码的个数也被确定.In this paper,we present a factorization of xqn+1-λover Fq2 and the enumeration of self-conjugate-reciprocal monic polynomials over Fq2,where q is a prime power andλ∈Fq*.Furthermore,we propose the explicit number of monic self-conjugate-reciprocal irreducible factors of xn+1.As an application to negacyclic codes,the number of linear Hermitian complementary dual negacyclic codes has been evaluated.

关 键 词：有限域 自共轭互反多项式 负循环码 厄米特互补对偶负循环码 

分 类 号：O174.14[理学—数学]