Construction of cyclic one-step majority-logic decodable codes using genetic algorithms

In [6], a construction of cyclic one-step majority-logic decodable codes based on idempotent polynomials is given. However, the search for the feasible Parity-Check Idempotent runs through all possible combinations of cyclotomic cosets modulo n, satisfying some algebraic constraints, consequently, increasing the code length may result in very large dimension space search, and the search for the solution becomes more difficult. In this paper, we propose a Genetic Algorithm that aimes to construct new moderate and high lengths Binary Cyclic OSMLD codes, considered as LDPC codes, with high correction capacities. Our construction is very efficient and provide codes with high lenghts and high rates.