Negacyclic codes of length $8p^s$ over $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$
Bull. Korean Math. Soc. 2019 Vol. 56, No. 6, 1385-1422
Published online October 17, 2019
Printed November 30, 2019
Chakkrid Klin-eam, Jirayu Phuto
Naresuan University; Naresuan University
Abstract : Let $p$ be an odd prime. The algebraic structure of all negacyclic codes of length $8p^s$ over the finite commutative chain ring $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$ where $u^2=0$ is studied in this paper. Moreover, we classify all negacyclic codes of length $8p^s$ over $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$ into 5 cases, i.e., $p^m\equiv 1 \pmod{16}$, $p^m\equiv 3,11 \pmod{16}$, $p^m\equiv 5,13 \pmod{16}$, $p^m\equiv 7,15 \pmod{16}$ and $p^m\equiv 9 \pmod{16}$. From that, the structures of dual and some self-dual negacyclic codes and number of codewords of negacyclic codes are obtained.
Keywords : negacyclic codes, finite chain rings, constacyclic codes, repeated-root codes
MSC numbers : Primary 94B15, 94B05; Secondary 11T71
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