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Construction of LCD codes from tridiagonal Toeplitz matrices | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 09 تیر 1405 | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2026.30942.2674 | ||
| نویسندگان | ||
| Wajid M. Shaikh1، 2؛ Rupali S. Jain1؛ B. Surendranath Reddy* 1؛ Bhagyashri S. Patil1، 3 | ||
| 1School of Mathematical Sciences, SRTMU Nanded, India | ||
| 2P.E.S. College of Engineering, Chhatrapati Sambhajinagar, India | ||
| 3MGM’s College of Engineering, Nanded, India | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| LCD code؛ Toeplitz matrix؛ Dickson polynomial | ||
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