Binary Linear Codes from the Group A₅

Cedric Wanjala Ndarinyo¹ Lucy Chikamai²& Shem Aywa³
Kibabii University

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 Citation: KIBU Conference (2017). Innovative Research and Knowledge for Global Competitiveness and Sustainable Development. Proceedings of 2nd Interdisciplinary International Scientific Conference 14 – 15 June 2017. Kibabii University Main campus, Bungoma Kenya  ISBN: 978-9966-59-011-4

Abstract

We examine all of the binary codes constructed from the primitivepermutation representations of the group  of degrees 5, 6  and 10 using modular representation method ,determine the properties of codes obtained and establish the relationship of these codes  with some designs and graphs. We use Magma and meat axe softwares to determine the irreducibility of the maximal modules. We develop algorithms that determine these codes and add the algorithms to the Magma software. These codes will be used in communication channels for error detection and error correction.

Mathematics Subject Classification: 05E15, 05E20, 05B05.

Key Words: Binary Codes, Combinatorics, Designs and Graphs, Modules

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