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Ternary codes of steiner triple systems
Authors:J D Key
Abstract:The code over a finite field Fq of a design ?? is the space spanned by the incidence vectors of the blocks. It is shown here that if ?? is a Steiner triple system on v points, and if the integer d is such that 3dv < 3d+1, then the ternary code C of ?? contains a subcode that can be shortened to the ternary generalized Reed-Muller code ?F3(2(d ? 1),d) of length 3d. If v = 3d and d ≥ 2, then C? ? ?F3(1,d)? ? F3(2(d ? 1),d) ? C. © 1994 John Wiley & Sons, Inc.
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