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LCD codes from tridiagonal Toeplitz matrices
Finite Fields and Their Applications ( IF 1.2 ) Pub Date : 2021-07-07 , DOI: 10.1016/j.ffa.2021.101892 Minjia Shi 1 , Ferruh Özbudak 2 , Li Xu 3 , Patrick Solé 4
中文翻译:
来自三对角 Toeplitz 矩阵的 LCD 代码
更新日期:2021-07-07
Finite Fields and Their Applications ( IF 1.2 ) Pub Date : 2021-07-07 , DOI: 10.1016/j.ffa.2021.101892 Minjia Shi 1 , Ferruh Özbudak 2 , Li Xu 3 , Patrick Solé 4
Affiliation
Double Toeplitz (DT) codes are codes with a generator matrix of the form with T a Toeplitz matrix, that is to say constant on the diagonals parallel to the main. When T is tridiagonal and symmetric we determine its spectrum explicitly by using Dickson polynomials, and deduce from there conditions for the code to be LCD. Using a special concatenation process, we construct optimal or quasi-optimal examples of binary and ternary LCD codes from DT codes over extension fields.
中文翻译:
来自三对角 Toeplitz 矩阵的 LCD 代码
双托普利兹 (DT) 代码是具有以下形式的生成矩阵的代码 与Ť一个托普利兹矩阵,也就是说平行于主对角线上是恒定的。当T为三对角对称时,我们使用 Dickson 多项式明确确定其频谱,并从中推导出代码为 LCD 的条件。使用特殊的连接过程,我们从扩展字段上的 DT 代码构建二进制和三进制 LCD 代码的最佳或准最佳示例。