Bounds on code parameters

Theorem 3 yields a description of the coset leaders of a code  $\mathfrak{G}_{k}^{}$ in terms of the coset leaders of its predecessor $\mathfrak{G}_{k-1}^{}$ in the $\mathfrak{G}$-construction. The maximum weight coset leader of $\mathfrak{G}_{k}^{}$, in turn, determines the covering radius of this $\ensuremath{{\mathfrak{G}}}$-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.