LCD codes from tridiagonal Toeplitz matrices

Double Toeplitz (DT) codes are with a generator matrix of the form (I,T) T matrix, that is to say constant on diagonals parallel main. When tridiagonal and symmetric we determine its spectrum explicitly by using Dickson polynomials, deduce from there conditions for code be LCD. Using special concatenation process, construct optimal or quasi-optimal examples binary ternary LCD DT over extension fields.