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Journal Articles Finite Fields and Their Applications Year : 2021

LCD CODES FROM TRIDIAGONAL TOEPLITZ MATRICES

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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Dates and versions

hal-03368476 , version 1 (06-10-2021)

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Attribution - NonCommercial - NoDerivatives

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Minjia Shi, Ferruh Özbudak, Li Xu, Patrick Solé. LCD CODES FROM TRIDIAGONAL TOEPLITZ MATRICES. Finite Fields and Their Applications, 2021, 75, pp.101892. ⟨10.1016/j.ffa.2021.101892⟩. ⟨hal-03368476⟩
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