Ternary codes of steiner triple systems

The code over a finite field F^q 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 3^d ≤ v < 3^d+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 3^d. If v = 3^d and d ≥ 2, then C_? ? ?_F3(1,d)? ? _F3(2(d ? 1),d) ? C. © 1994 John Wiley & Sons, Inc.