具有任意数量广义Niho型零点的循环码的重量分布及勘误
Weight distribution of cyclic codes with arbitrary number of generalized Niho type zeroes with corrigendum
摘要：
循环码是一类重要的线性码，其码重分布已被广泛研究。迄今为止获得的大多数先前结果都是针对不超过三个零的循环码。受\cite{Li-Zeng-Hu}和\cite{gegeng2}的启发，我们研究了$\mathbb{F}_p$上的两类广义Niho型循环码，即$t+1$的零的$\ca$（对于$p=2$）和$t$的零的$\cb$（对于任何素数$p$）.我们发现，第一个家庭有至多$(2t+1)$非零的权重，第二个有至多$2t$非零的权重。文中还确定了它们的重量分布。
英文摘要：
Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. Most previous results obtained so far were for cyclic codes with no more than three zeroes. Inspired by the works \cite{Li-Zeng-Hu} and \cite{gegeng2}, we study two families of cyclic codes over $\mathbb{F}_p$ with arbitrary number of zeroes of generalized Niho type, more precisely $\ca$ (for $p=2$) of $t+1$ zeroes, and $\cb$ (for any prime $p$) of $t$ zeroes for any $t$. We find that the first family has at most $(2t+1)$ non-zero weights, and the second has at most $2t$ non-zero weights. Their weight distribution are also determined in the paper.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
