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Journal of Applied Mathematics and Computing

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07-06-2018 | Original Research

Study on negacyclic codes over the ring \(\mathbb {Z}_{p}[u]/<u^{k+1}-u\)

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2019

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Abstract

In this paper, we study the properties of negacyclic codes over the ring \(R=\mathbb {Z}_{p}+u\mathbb {Z}_{p}+\dots +u^k\mathbb {Z}_{p} \), for odd prime p, using decomposition method. We have determined the generators of negacyclic and dual negacyclic codes. We have also established the necessary and sufficient condition for it to contains it’s dual. It is also shown that the \(\mathbb {Z}_p\)-Gray image of a negacyclic code of length n is a quasi negacyclic code of length 3n.

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Title: Study on negacyclic codes over the ring
Publication date: 07-06-2018
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2019
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-018-1197-5

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