@article { author = {Rafieepour, A. and Mazrooei, M.}, title = {SOME NEW CONSTRUCTIONS OF LINEAR CODES INCLUDING A WIDE FAMILY OF MDS CODES}, journal = {Journal of Algebraic Systems}, volume = {7}, number = {2}, pages = {291-300}, year = {2020}, publisher = {Shahrood University of Technology}, issn = {2345-5128}, eissn = {2345-511X}, doi = {10.22044/jas.2019.7004.1343}, 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.}, keywords = {Finite Fields,Linear Codes,MDS codes}, url = {https://jas.shahroodut.ac.ir/article_1598.html}, eprint = {https://jas.shahroodut.ac.ir/article_1598_8c556522c1aaf88d9e80bdbe10f287f4.pdf} }