Theorem 2.5 yields a description of the coset leaders of
G k in terms of the coset leaders of its predecessor
G k-1 in the G-construction. The maximum weight coset leader
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.
Bounds on code parameters