Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 21 Issue 4

© 2021. Ted Hurley, Donny Hurley & Barry Hurley. This research/review article is distributed under the terms of the Attribution- NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). You must give appropriate credit to authors and reference this article if parts of the article are reproduced in any manner. Applicable licensing terms are at https://creativecommons.org/ licenses/by-nc-nd/4.0/. Maximum Distance Separable Codes to Order By Ted Hurley, Donny Hurley & Barry Hurley Institute of Technology Abstract- Maximum distance separable (MDS) are constructed to required specifications. The codes are explicitly given over finite fields with efficient encoding and decoding algorithms. Series of such codes over finite fields with ratio of distance to length approaching (1 − R ) for given R , 0 < R < 1 are derived. For given rate R = r n, with p not dividing n, series of codes over finite fields of characteristic p are constructed such that the ratio of the distance to the length approaches (1 − R ). For a given field GF(q) MDS codes of the form ( q −1, r ) are constructed for any r . The codes are encompassing, easy to construct with efficient encoding and decoding algorithms of complexity max{ O ( n log n ), t 2 }, where t is the error-correcting capability of the code. GJSFR-F Classification: MSC 2010: 00A69 MaximumDistanceSeparableCodestoOrder Strictly as per the compliance and regulations of: Global Journal of Science Frontier Research: F Mathematics and Decision Sciences Volume 21 Issue 4 Version 1.0 Year 2021 Type: Double Blind Peer Reviewed International Research Journal Publisher: Global Journals Online ISSN: 2249-4626 & Print ISSN: 0975-5896