SOME NEW CONSTRUCTIONS OF LINEAR CODES INCLUDING A WIDE FAMILY OF MDS CODES

Document Type: Original Manuscript

Authors

Department of Mathematical Sciences, University of Kashan, P.O. Box 87317- 53153, Kashan, Iran.

Abstract

Let ‎$‎\mathbb{Z}_p‎$‎ be the finite field of integers modulo ‎$‎p‎$‎, where ‎$‎p>3‎$‎ is a prime integer. This paper presents new constructions of linear codes over ‎$‎\mathbb{Z}_p‎$‎‎. Based on our construction, linear codes of length ‎$‎p-1‎$‎, including a wide family of MDS codes, and codes of length ‎$‎(p-1)^2‎$ ‎are ‎constructed.‎ we shall discuss the parameters of the codes defined while describing a generator matrix for the first family.

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