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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 diagonalsparallel to the main. When $T$ is tridiagonal and symmetric we determine itsspectrum explicitly by using Dickson polynomials, and deduce from thereconditions for the code to be LCD. Using a special concatenation process, weconstruct optimal or quasi-optimal examples of binary and ternary LCD codesfrom DT codes over extension fields.

LCD Codes from tridiagonal Toeplitz matrice