Construction and decoding of OSMLD codes derived from unital and oval designs

Abstract

A construction of One-Step Majority-Logic Decodable (OSMLD) codes based on the incidence matrices of Balanced Incomplete Block Designs (BIBD) is given. In this paper, we focus on unital and oval designs which are constructed from a Projective Geometry (PG). Thus, we derive from the unital and oval designs new systematic and non-systematic OSMLD codes with rates and lengths not available with existing OSMLD codes. Simulation results show that the derived codes converge well under Iterative Threshold Decoding with an efficient trade-off between complexity and performances.