finite fields, linear codes, mds codes, Mathematics, QA1-939
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.