Bounds on code parameters

Theorem 2.5 yields a description of the coset leaders of a code  G k in terms of the coset leaders of its predecessor G k-1 in the G-construction. The maximum weight coset leader of G k, in turn, determines the covering radius of this G-code and, hence, the code parameters of the subsequent codes in the construction. This insight allows us to improve the known bounds on the parameters of lexicodes.