Ternary codes of steiner triple systems
Jennifer D. Key Β· Journal of Combinatorial Designs Β· 1994
Abstract The code over a finite field Fq of a design π is the space spanned by the incidence vectors of the blocks. It is shown here that if π is a Steiner triple system on v points, and if the integer d is such that 3d β€ v < 3d+1, then the ternary code C of π contains a subcode that can be shortened to the ternary generalized ReedβMuller code βF3(2(d β 1),d) of length 3d. If v = 3d and d β₯ 2, then Cβ β βF3(1,d)β β F3(2(d β 1),d) β C. Β© 1994 John Wiley & Sons, Inc.