| 杨仕椿,廖群英.与对角格空时码相关的一类mathbb{Z}[zeta_{m}]上不可约多项式的判别式[J].数学年刊A辑,2021,42(2):149~158 |
| 与对角格空时码相关的一类mathbb{Z}[zeta_{m}]上不可约多项式的判别式 |
| The Determinant of a Class of Irreducible Polynomials over Z[ζm] Related to Lattice-Based Diagonal Space-Time Block Codes |
| Received:April 12, 2020 Revised:November 20, 2020 |
| DOI：10.16205/j.cnki.cama.2021.0012 |
| 中文关键词: 判别式 不可约多项式 Pell方程 对角格空时码 |
| 英文关键词:Determinant Irreducible polynomial Pell equation Lattice-Based diagonal space-time block code |
| 基金项目: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)和四川省高校科研创新团队建设计划(No.,18TD0047) |
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| 中文摘要: |
| 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mathbb{Z}[zeta_{m}]上的一类二次不可约多项式的判别式Delta,确定了mathbb{Z}[zeta_{m}]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,Delta的值可以任意小. 最后,提出几个关于mathbb{Z}[zeta_{m}]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. |
| 英文摘要: |
| 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. |
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