Codes from hall planes of odd order

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

doi:10.3934/amc.2017011

Codes from hall planes of odd order

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	179-185
Number of pages	7
Journal	Advances in Mathematics of Communications
Volume	11
Issue number	1
DOIs	https://doi.org/10.3934/amc.2017011
Publication status	Published - 01 Feb 2017

Keywords

Codes
Hamada-Sachar conjecture
Non-desarguesian planes

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KW - Non-desarguesian planes

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Codes from hall planes of odd order

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