Majority logic decoding using combinatorial designs (Corresp.)

If the vectors of some constant weight in the dual of a binary linear code support a (\nu,b,r,k,\lambda) balanced incomplete block design (BIBD), then it is possible to correct [(r + 2 - 1)/2\lambda] errors with one-step majority logic decoding. This bound is generalized to the case when the vectors of certain constant weight in the dual code support a t -design. With the aid of this bound, the one-step majority logic decoding of the first, second, and third order Reed-Muller codes is examined.