Codes from hall planes of odd order | Zendy

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

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Codes from hall planes of odd order

Author(s) -

J. D. Key,

T. P. McDonough,

V. C. Mavron

Publication year - 2017

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2017011

Subject(s) - mathematics , dimension (graph theory) , ternary operation , plane (geometry) , code (set theory) , order (exchange) , projective plane , ternary golay code , dual (grammatical number) , combinatorics , word (group theory) , pure mathematics , geometry , linear code , algorithm , block code , computer science , linguistics , programming language , philosophy , decoding methods , set (abstract data type) , finance , economics , correlation

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.Peer reviewe

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