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On a Class of Constacyclic Codes of Length 2ps over Fpm[u]/⟨ua⟩

Authors: 

Hai Q. Dinh, Bac Trong Nguyen, and Songsak Sriboonchitta

Source title: 
Bulletin of the Korean Mathematical Society, 55(4): 1189-1208, 2018 (ISI)
Academic year of acceptance: 
2018-2019
Abstract: 

The aim of this paper is to study the class of $\Lambda$-constacyclic codes of length $2p^s$ over the finite commutative chain ring ${\mathcal R}_a=\frac{\mathbb F_{p^m}[u]}{\left\langle u^a \right\rangle}=\mathbb F_{p^m} + u \mathbb F_{p^m}+ \dots + u^{a-1}\mathbb F_{p^m}$, for all units $\Lambda$ of $\mathcal R_a$ that have the form $\Lambda=\Lambda_0+u\Lambda_1+\dots+u^{a-1}\Lambda_{a-1}$, where $\Lambda_0, \Lambda_1, \dots, \Lambda_{a-1} \in \mathbb F_{p^m}$, $\Lambda_0 \,{\not=}\, 0, \, \Lambda_1 \,{\not=}\, 0$. The algebraic structure of all $\Lambda$-constacyclic codes of length $2p^s$ over ${\mathcal R}_a$ and their duals are established. As an application, this structure is used to determine the Rosenbloom-Tsfasman (RT) distance and weight distributions of all such codes. Among such constacyclic codes, the unique MDS code with respect to the RT distance is obtained.