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Let \(\mathcal {R}_{m}= \mathbb {F}_{p^{r}}[v]/< v^{m} - v>\) , where p is an odd prime, \(\mathbb {F}_{p^{r}}\) is a finite field with \(p^{r}\) elements, \(m-1|p-1\) and and \( v^{m} = v\) . In this study, we investigate quantum codes over \(\mathbb {F}_{p^{r}}\) by using constacyclic codes over \(\mathcal {R}_{m}\) , which are dual containing. Furthermore, by using cyclic codes over the ring \(\mathcal {R}_{m}\) and their decomposition over the finite field \(\mathbb {F}_{p^{r}}\) into cyclic codes, a LCD codes are given as images of LCD codes over \(\mathcal {R}_{m}\) .

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On Quantum and LCD Codes from the Consatacyclic and Cyclic Codes Over the Ring \(\mathbb {F}_{p^{r}}[v]/< v^{m} - v>\)

  • 会议论文

  • 发表日期：

    2025年

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  • Mohammed Sabiri,
  • Bassou Aouijil

摘要

Let \(\mathcal {R}_{m}= \mathbb {F}_{p^{r}}[v]/< v^{m} - v>\) , where p is an odd prime, \(\mathbb {F}_{p^{r}}\) is a finite field with \(p^{r}\) elements, \(m-1|p-1\) and and \( v^{m} = v\) . In this study, we investigate quantum codes over \(\mathbb {F}_{p^{r}}\) by using constacyclic codes over \(\mathcal {R}_{m}\) , which are dual containing. Furthermore, by using cyclic codes over the ring \(\mathcal {R}_{m}\) and their decomposition over the finite field \(\mathbb {F}_{p^{r}}\) into cyclic codes, a LCD codes are given as images of LCD codes over \(\mathcal {R}_{m}\) .