Majority logic decoding using combinatorial designs (Corresp.)
M. M. Hafizur Rahman, Ian F. Blake · IEEE Transactions on Information Theory · 1975
If the vectors of some constant weight in the dual of a binary linear code support a( u,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 at-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.