LCD codes from tridiagonal Toeplitz matrices

2021-10-01
Shi, Minjia
Özbudak, Ferruh
Xu, Li
Solé, Patrick
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.
Finite Fields and their Applications

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Citation Formats
M. Shi, F. Özbudak, L. Xu, and P. Solé, “LCD codes from tridiagonal Toeplitz matrices,” Finite Fields and their Applications, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85109170073&origin=inward.