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Assume that \(p^n \equiv 3\pmod 4\) and \(\alpha =\alpha _0+u\alpha _1+\cdots +u^{t-1}\alpha _{t-1}\) is Type 1 unit in \(\mathbb {F}_{p^n}+u\mathbb {F}_{p^n}+\cdots +u^{t-1}\mathbb {F}_{p^n} (u^t=0),\) where p is an odd prime, n is a positive integer and \(\alpha _0,\alpha _1,\ldots ,\alpha _{t-1} \in \mathbb {F}_{p^n}, \alpha _0\ne 0, \alpha _1\ne 0.\) In this paper, for \(p^n \equiv 3\pmod 4\) , we determine Hamming distances and RT distances of all Type 1 \(\alpha \) -constacyclic codes of length \(4p^s\) over the chain ring \(\mathbb {F}_{p^n}+u\mathbb {F}_{p^n}+\cdots +u^{k-1}\mathbb {F}_{p^n}\) with the help of generator polynomials of these codes and their duals.

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On Hamming Distance and RT Distance of a Class of Constacyclic Codes over  \(\mathbb {F}_{p^n}+u\mathbb {F}_{p^n}+\cdots +u^{t-1}\mathbb {F}_{p^n}\)

  • 会议论文

  • 发表日期：

    2025年

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  • Saroj Rani

摘要

Assume that \(p^n \equiv 3\pmod 4\) and \(\alpha =\alpha _0+u\alpha _1+\cdots +u^{t-1}\alpha _{t-1}\) is Type 1 unit in \(\mathbb {F}_{p^n}+u\mathbb {F}_{p^n}+\cdots +u^{t-1}\mathbb {F}_{p^n} (u^t=0),\) where p is an odd prime, n is a positive integer and \(\alpha _0,\alpha _1,\ldots ,\alpha _{t-1} \in \mathbb {F}_{p^n}, \alpha _0\ne 0, \alpha _1\ne 0.\) In this paper, for \(p^n \equiv 3\pmod 4\) , we determine Hamming distances and RT distances of all Type 1 \(\alpha \) -constacyclic codes of length \(4p^s\) over the chain ring \(\mathbb {F}_{p^n}+u\mathbb {F}_{p^n}+\cdots +u^{k-1}\mathbb {F}_{p^n}\) with the help of generator polynomials of these codes and their duals.