LCD codes from tridiagonal Toeplitz matrices


Shi M., ÖZBUDAK F., Xu L., Solé P.

Finite Fields and their Applications, vol.75, 2021 (Peer-Reviewed Journal) identifier identifier

  • 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, Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, MathSciNet, zbMATH
  • Keywords: LCD codes, Toeplitz matrices, Dickson polynomials, LINEAR CODES, EQUIVALENT

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.