IJPAM: Volume 94, No. 1 (2014)

ON THE GENERATORS OF CYCLIC CODES
OVER $\mathbb{Z}_{m}$ OF ANY LENGTH $n$

Louis Beaugris
Department of Mathematics
C-233, Kean University
1000 Morris Ave, Union, New Jersey, USA


Abstract. Over the last two decades, there have been discoveries of various good codes over the rings $\mathbb{Z}_{m}$ of integers modulo $m$. Restrictions have been imposed on the code's alphabet size $m$ and over the code's length $n$ for many reasons. This paper shows a construction of the generators of cyclic codes over $\mathbb{Z}_{m}$ via the Division Algorithm, with no restrictions on the aforementioned code parameters.

Received: April 2, 2014

AMS Subject Classification: 94B15

Key Words and Phrases: cyclic codes, generators, principal ideals, division algorithm

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DOI: 10.12732/ijpam.v94i1.8 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 94
Issue: 1
Pages: 71 - 80

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).