Double Toeplitz (DT) codes are codes with a generator matrix of the form $(I,T)$ 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.

翻译：Toeplitz (DT) 双倍代码是带有美元(I,T) 和美元(T) 的生成器矩阵的代码,Teplitz 矩阵是指在正对角与正对角的常数。当$T是三对角和对称时,我们通过使用Dickson 多元倍数来明确确定其频谱,并从中推断出代码是LCD的条件。我们使用特殊的组合程序,从扩展域中构建了来自DT代码的二进制和代代号的最佳或准最佳实例。