LCD codes from tridiagonal Toeplitz matrices

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 conditi...

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Bibliographic Details
Published in:Finite fields and their applications 2021-10, Vol.75, p.101892, Article 101892
Main Authors: Shi, Minjia, Özbudak, Ferruh, Xu, Li, Solé, Patrick
Format: Article
Language:English
Subjects:
Computer Science
Dickson polynomials
Information Theory
LCD codes
Toeplitz matrices
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Summary: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.
ISSN:1071-5797
1090-2465
DOI:10.1016/j.ffa.2021.101892