Codes from hall planes of odd order

J. D. Key; T. P. McDonough; V. C. Mavron

doi:10.3934/amc.2017011

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2017, Volume 11, Issue 1: 179-185. Doi: 10.3934/amc.2017011

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Codes from hall planes of odd order

Institute of Mathematics, Physics and Computer Science, Aberystwyth University, Aberystwyth SY23 3BZ, UK

Received: August 2015

Published online: February 2017

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Abstract

We show explicitly that the dimension of the ternary code of the Hall plane of order 9 is greater than the dimension of the ternary code of the desarguesian plane of order 9. The proof requires finding a word with some defined properties in the dual ternary code of the desarguesian plane of order 9. The idea can be generalised for other orders, provided that words in the dual code of the desarguesian projective plane that have the specified properties can be found.

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Mathematics Subject Classification: Primary: 94B05, 51A35; Secondary: 05B05.

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References

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