LCD codes from tridiagonal Toeplitz matrices

Shi M., ÖZBUDAK F., Xu L., Solé P.

Finite Fields and their Applications, cilt.75, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 75
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1016/j.ffa.2021.101892
  • Dergi Adı: Finite Fields and their Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, MathSciNet, zbMATH
  • Anahtar Kelimeler: LCD codes, Toeplitz matrices, Dickson polynomials, LINEAR CODES, EQUIVALENT
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

© 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.