In 2021, Shi et al. established essential and adequate conditions for a Double Toeplitz code of LCD when the Toeplitz matrix, T, is symmetric and tri-diagonal. In continuation to this, K. Cheng in 2024 found the conditions under which a Double Toeplitz code is LCD when T is a skew-symmetric and tri-diagonal matrix, leveraging results on factoring Dickson polynomials over finite fields. Additionally, Cheng et al. introduced a technique to build LCD codes with arbitrary least distance from DT codes over extension fields by employing concatenation, adjusting the length if necessary. In the present study, we have shown that the power of a skew- symmetric tridiagonal Toeplitz matrix does not yield another skew-symmetric tridiagonal Toeplitz matrix. Subsequently, we employ concatenation to construct an LCD code.
| Published in | Abstract Book of the National Conference on Advances in Basic Science & Technology |
| Page(s) | 110-110 |
| Creative Commons |
This is an Open Access abstract, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2025. Published by Science Publishing Group |
LCD Codes, Toeplitz Matrix, DT Codes
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