LCD codes from tridiagonal Toeplitz matrices

Date

2021-10-01

Author

Shi, Minjia
Özbudak, Ferruh
Xu, Li
Solé, Patrick

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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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.

Subject Keywords

LCD codes, Toeplitz matrices, Dickson polynomials

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85109170073&origin=inward
https://hdl.handle.net/11511/91353

Journal

Finite Fields and their Applications

DOI

https://doi.org/10.1016/j.ffa.2021.101892

Collections

Department of Mathematics, Article

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Citation Formats

M. Shi, F. Özbudak, L. Xu, and P. Solé, “LCD codes from tridiagonal Toeplitz matrices,” Finite Fields and their Applications, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85109170073&origin=inward.