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

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.

کلیدواژه ها:

Finite Fields ، Linear Codes ، MDS codes