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Ternary codes of steiner triple systems

✍ Scribed by J. D. Key

Publisher: John Wiley and Sons
Year: 1994
Tongue: English
Weight: 339 KB
Volume: 2
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.3180020105

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✦ Synopsis

The code over a finite field F, of a design D is the space spanned by the incidence vectors of the blocks. It is shown here that if D is a Steiner triple system on v points, and if the integer

then the ternary code C of contains a subcode that can be shortened to the ternary generalized Reed-Muller code R ~~( 2 ( d l), d ) of length 3d. If v = 3d and d 2 2, then C* R F ~( ~, d ) C R ~~( 2 ( d -I), d ) C .

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