Modular Representation of the Unitary Group U3 (4) As Linear Codes

Modular Representation of the Unitary Group U3 (4) As Linear Codes

Janet Lilian Maina1 Lucy Chikamai2& Lydia Njuguna3
1,2-Kibabii University,

3-Kenyatta 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

Coding theory deals with methods of constructing and analyzing error-correcting codes and decoding them in an efficient manner. In this paper, we construct some binary linear codes from modular representation of Unitary U3(4) and determine  their properties. We aim to determine linear codes from primitive permutation representations of U3(4)  group using modular representation method ,determine the properties of codes obtained from U3(4)  group and to establish the relationship of these codes  with some designs, graphs and finite geometries. We use Magma and meat axe softwares to determine irreducibility of modules. We develop algorithm that determine these codes and add the algorithm to the Magma software. The codes constructed from this group are used in the encoding and decoding of messages, error detection and error correction.

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

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

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