LCD codes from tridiagonal Toeplitz matrices
Finite Fields and their Applications, vol.75, 2021 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 75
- Publication Date: 2021
- Doi Number: 10.1016/j.ffa.2021.101892
- Journal Name: Finite Fields and their Applications
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, MathSciNet, zbMATH
- Keywords: LCD codes, Toeplitz matrices, Dickson polynomials, LINEAR CODES, EQUIVALENT
- Middle East Technical University Affiliated: Yes
Abstract
© 2021 Elsevier Inc.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.