On Asymptotic Ensemble Weight Enumerators of Multi-Edge Type Codes

In this paper, we investigate the asymptotic ensemble weight enumerators of multi-edge type codes whose component codes are arbitrary block codes. Two forms of asymptotic growth rate of codewords, corresponding to the primal and dual problems, are obtained. Furthermore, for the codewords of small linear-sized weights, we develop a simplification method to restrict the search space of the primal problem and study the optimality conditions of the dual problem, giving a first-order approximation of the growth rate and a condition of exponentially few small weight codewords.