Optimal and suboptimal structured algorithms of binary linear block codes

The optimal and suboptimal structured algorithms of linear block codes from the geometrical perspective are represented. The minimum distance and weight property lemmas and the theorem are proved for the generator matrix. Based upon the property of generator matrix, the structured algorithms of linear block codes are demonstrated. Since the complexity of optimal structured algorithm is very high, the binary linear block codes is searched by using the suboptimal structured algorithm. The comparison with Bose-Chaudhuri-Hocquenqhem (BCH) codes shows that the searched linear block codes are equivalent on minimum distance and can be designed for more block lengths. Because the linear block codes are used widely in communication systems and digital applications, the optimal and suboptimal structured algorithms must have great future being widely used in many applications and perspectives.