LCD codes from tridiagonal Toeplitz matrices
Finite Fields and their Applications, cilt.75, 2021 (SCI-Expanded, Scopus)
- 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.