Majority Logic Decoding With Subspace Designs

Rudolph (1967) introduced one-step majority logic decoding for linear codes derived from combinatorial designs. The decoder is easily realizable in hardware and requires that the dual code has to contain blocks of so called geometric designs as codewords. Peterson Weldon (1972) extended Rudolph's algorithm a two-step correcting same number errors Reed's celebrated multi-step decoder. Here, we study subspace It turns out these have capability designs, but their complexity sometimes drastically improved. For known infinite series reduction exponential.