The Binary Linear Codes of Mathieu Group M_24

The Binary Linear Codes of Mathieu Group

Vincent Nyongesa Marani1Lucy Chikamai2& Prof. Shem Aywa 3
1,2,3-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 use coding theory to study the internal structure of simple groups. Coding theory deals with methods of constructing and analyzing error-correcting codes. In this paper, we construct all binary linear codes from  and determine their properties. We link these codes to designs and graphs.We develop the algorithm that determine these codes and add the algorithm to the Magma software.

Mathematics Subject Classification: 05B05, 20D45, 94B05

Key words: Binary codes, designs and Modules.

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