TY - JOUR ID - 1598 TI - SOME NEW CONSTRUCTIONS OF LINEAR CODES INCLUDING A WIDE FAMILY OF MDS CODES JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Rafieepour, A. AU - Mazrooei, M. AD - Department of Mathematical Sciences, University of Kashan, P.O. Box 87317- 53153, Kashan, Iran. Y1 - 2020 PY - 2020 VL - 7 IS - 2 SP - 291 EP - 300 KW - Finite Fields KW - Linear Codes KW - MDS codes DO - 10.22044/jas.2019.7004.1343 N2 - 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. UR - https://jas.shahroodut.ac.ir/article_1598.html L1 - https://jas.shahroodut.ac.ir/article_1598_8c556522c1aaf88d9e80bdbe10f287f4.pdf ER -