Generalized Cascade Codes

A cascade method of constructing block codes from several initial (linear or nonlinear) codes is presented. The generalized cascade codes thus constructed are in many respects closer to the optimal codes than the codes given in Sloane’s table. For lengths $n<200$ and distances $7\leq d\leq 29$, around 60 such codes are constructed, with the result that more than 300 values from Sloane’s table can be improved.