On Construction and Performance Evaluation of (4096, 815, 3162) Hermitian Code

Authors

Richard Adusei, Department of Mathematics, University for Development Studies, GhanaFollow
Mohammed Muniru Iddrisu, Department of Mathematics, University for Development Studies, GhanaFollow

Author Country (or Countries)

Ghana

Abstract

Algebraic Geometry is a branch of mathematics applied in so many disciplines including Coding Theory. This paper focuses on the construction, performance evaluation and practical implementation of encoding and decoding processes of codes constructed from Hermitian Curves. These codes also known as Hermitian codes are types of Algebraic Geometric codes. In this work, performance of the code is done by simulating the (4096, 815, 3162) hermitian code constructed from a hermitian curve using techniques from algebraic geometry with a (255,153,103) Reed-Solomon code from the same $GF(256)$ . The decoding process uses Berlekamp-Massay-Sakata (BMS) algorithm, Majority Voting and Forney algorithm. The stages and algorithm were also implemented using the Python programming language.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140110

Recommended Citation

Adusei, Richard and Muniru Iddrisu, Mohammed (2020) "On Construction and Performance Evaluation of (4096, 815, 3162) Hermitian Code," Applied Mathematics & Information Sciences: Vol. 14: Iss. 1, Article 10.
DOI: http://dx.doi.org/10.18576/amis/140110
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss1/10