Abstract
In this paper, we consider the construction of new classes of linear codes over the ring \(R_{q,p,m}={\mathbb {Z}}_{p^{m}}[u_{1}, u_{2}, \ldots , u_{ q}]/\left\langle u_{i}^{2}=0,u_{i}u_{j}=u_{j}u_{i}\right\rangle \) for \(i\ne j\) and \(1 \le i,j \le q\). The simplex and MacDonald codes of types \(\alpha \) and \(\beta \) are obtained over \(R_{q,p,m}\). We characterize some linear codes over \({\mathbb {Z}}_{p^{m}}\) that are the torsion codes and Gray images of these simplex and MacDonald codes, and determine the minimal codes.
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Communicated by Masaaki Harada.
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Chatouh, K., Guenda, K. & Gulliver, T.A. New classes of codes over \(R_{q,p,m}={\mathbb {Z}}_{p^{m}}[u_{1}, u_{2}, \ldots , u_{ q}]/\left\langle u_{i}^{2}=0,u_{i}u_{j}=u_{j}u_{i}\right\rangle \) and their applications. Comp. Appl. Math. 39, 152 (2020). https://doi.org/10.1007/s40314-020-01181-z
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DOI: https://doi.org/10.1007/s40314-020-01181-z