Theorem 3 yields a description of the coset leaders of
a code
in terms of the coset leaders of its predecessor
in the
-construction.
The maximum weight coset leader of
, in turn,
determines the covering radius of this
-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.

**Subsections**