与对角格空时码相关的一类Z[ζm]上不可约多项式的判别式  

The Det erminant of a Class of Irreducible Polynomials over Z[ζm]Related to Lattice-Based Diagonal Space-Time Block Codes

作　　者：杨仕椿 廖群英 YANG Shichun;LIAO Qunying(School of Mathematics,Aba Teachers University,Wenchuan 623002,Sichuan China;School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,China.)

机构地区：[1]阿坝师范学院数学学院,四川汶川623002 [2]四川师范大学数学科学学院,成都610066

出　　处：《数学年刊（A辑）》2021年第2期149-158,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11861001,No.12071321);四川省应用基础研究项目(No.2016JY0134,NO.2018JY0458);四川省高校科研创新团队建设计划(No.18TD0047)的资助.

摘　　要：为实现信号在空间的分集,关于格的空时分组码的设计近年来备受关注.通过研究与对角的格空时码相关的Z[ζm]上的一类二次不可约多项式的判别式|△|,确定了Z[ζm]上的格空时编码的正规分集乘积的大小.进而,利用Pell方程的解的性质,构造性地证明了m=5,8,10,12时,|△|的值可以任意小.最后,提出几个关于Z[ζm]上的二次不可约和三次不可约多项式的判别式大小的猜想.To achieve the diversity of the signal in space,the design of the case of spacetime block codes has attracted much attention in recent years.By studying the discriminant of a class of quadratic irreducible polynomials over Z[ζm]related to lattice-based diagonal space-time block codes,the authors determine the size of the normalized diversity product for constructing the lattice space time code over Z[ζm] Furthermore,based on the property for solutions of the Pell equation,it is proved that the absolute value of the discriminant can be arbitrarily small when m=5,8,10,12.And then for the quadratic or cubic irreducible polynomials over Z[ζm],some problems to be further studied are proposed.

关 键 词：判别式 不可约多项式 PELL方程 对角格空时码 

分 类 号：O156.1[理学—数学]