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arXiv · 2103.04407

LCD Codes from tridiagonal Toeplitz matrice

Minjia Shi·Ferruh Özbudak·Li Xu·Patrick Solé
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Abstract

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.

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Minjia Shi, Ferruh Özbudak, Li Xu, Patrick Solé. 2021-03-07. LCD Codes from tridiagonal Toeplitz matrice. https://arxiv.org/abs/2103.04407

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