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Binary duadic codes and their related codes with a square-root-like lower bound
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DOI：10.1007/s10623-025-01759-w.png)
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Abstract
En 中文
Binary cyclic codes have been a hot topic for a long time, and their study has made significant progress. As is well known, constructing infinite families of binary cyclic codes [n,n +/- 12]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[n,\frac{n\pm 1}{2}]$$\end{document} with good minimum distance remains a challenge. In this paper, we employ the BCH bound for cyclic codes to address an open problem regarding binary cyclic codes proposed by Liu et al (Finite Field Appl 91:102270, 2023). Specifically, we present binary duadic codes with parameters [2m-1,2m-1,d]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[2<^>m-1, 2<^>{m-1},d]$$\end{document}, where the minimum distance d exhibits a square-root-like lower bound. Furthermore, we determine the parameters for their duals and extended codes.
Keywords:
Cyclic code
Duadic code
Square-root-like lower bound
BCH bound
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1.2
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124
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