Construction of LCD codes from tridiagonal Toeplitz matrices

Articles in Press

Document Type : Original paper

Authors

1 School of Mathematical Sciences, SRTMU Nanded, India

2 P.E.S. College of Engineering, Chhatrapati Sambhajinagar, India

3 MGM’s College of Engineering, Nanded, India

Abstract

A Toeplitz matrix $T$ is characterized by having constant entries along diagonals parallel to the main diagonal. Double Toeplitz (DT) codes are linear codes whose generator matrix takes the form $(I, T)$, where $T$ is a Toeplitz matrix. In 2021, Shi et al. established the necessary and sufficient condition for a DT code to be an LCD, assuming that $T$ is symmetric. In 2024, Cheng obtained the necessary and sufficient condition for a DT code to be an LCD when $T$ is skew-symmetric. In this paper, we consider Toeplitz tridiagonal matrices that are neither symmetric nor skew-symmetric. We derive the necessary and sufficient condition under which a DT code is an LCD code, using the factorization of Dickson polynomials over finite fields. Furthermore, by applying concatenation techniques, we construct a family of LCD codes with arbitrary minimum distance.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 30 June 2026

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