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<p>Deep holes have been widely studied, and it is very important in the decoding of generalized RS codes. However, there are few works on constructing general linear codes based on deep holes. Therefore, we consider constructing binary linear codes by combining deep holes with BCH codes. In this paper, three classes of binary linear codes are constructed by deep holes combined with the 3-error-correcting binary primitive BCH code and their extended codes, respectively. Furthermore, the parameters and the weight distributions of these binary linear codes are obtained. Finally, some examples are presented by Magma experiments, which support the weight distributions of these binary linear codes. These experimental results coincide with the weight distributions of linear codes.</p>

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The weight distributions of three new classes of binary linear codes

  • 期刊论文

  • 发表日期：

    2025年9月5日

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  • Yang Yong

摘要

Deep holes have been widely studied, and it is very important in the decoding of generalized RS codes. However, there are few works on constructing general linear codes based on deep holes. Therefore, we consider constructing binary linear codes by combining deep holes with BCH codes. In this paper, three classes of binary linear codes are constructed by deep holes combined with the 3-error-correcting binary primitive BCH code and their extended codes, respectively. Furthermore, the parameters and the weight distributions of these binary linear codes are obtained. Finally, some examples are presented by Magma experiments, which support the weight distributions of these binary linear codes. These experimental results coincide with the weight distributions of linear codes.