LCD CODES FROM TRIDIAGONAL TOEPLITZ MATRICES

Minjia Shi (1) , Patrick Solé (2) , Li Xu (1) , Ferruh Ozbudak (3)

1 Anhui University [Hefei]
2 I2M - Institut de Mathématiques de Marseille
3 METU - Middle East Technical University [Ankara]

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.

Mots clés: LCD codes; Toeplitz matrices; Dickson polynomials AMS(2020) Math Sc. Cl. 94B05; 15B05; 12E10

Domaines: Théorie de l'information [cs.IT]

Minjia Shi, Patrick Solé, Li Xu, Ferruh Ozbudak. LCD CODES FROM TRIDIAGONAL TOEPLITZ MATRICES. Finite Fields and Their Applications, 2021. ⟨hal-03368476⟩