Up to a new invariant \(\mu (b)\), the complete b-symbol weight distribution of a particular kind of two-weight irreducible cyclic codes, was recently obtained by Zhu et al. (Des Codes Cryptogr 90(5):1113–1125, 2022). The purpose of this paper is to simplify and generalize the results of Zhu et al., and obtain the b-symbol weight distributions of all one-weight and two-weight semiprimitive irreducible cyclic codes.

中文翻译：

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所有半本原不可约循环码的b符号权重分布

Zhu 等人最近获得了一个新的不变量\(\mu (b)\)，一种特定类型的二权不可约循环码的完整b符号权分布。（Des Codes Cryptogr 90(5):1113–1125, 2022）。本文的目的是对Zhu等人的结果进行简化和推广，得到所有一权和二权半本原不可约循环码的b符号权分布。