American Institute of Mathematical Sciences

February  2017, 11(1): 179-185. doi: 10.3934/amc.2017011

Codes from hall planes of odd order

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

Received  August 2015 Published  February 2017

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.

Citation: J. D. Key, T. P. McDonough, V. C. Mavron. Codes from hall planes of odd order. Advances in Mathematics of Communications, 2017, 11 (1) : 179-185. doi: 10.3934/amc.2017011
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