  In this work we study a weak order ideal associated with the coset leaders of
a non-binary linear code. This set allows the incrementally computation of the
coset leaders and the definitions of the set of leader codewords. This set of
codewords has some nice properties related to the monotonicity of the weight
compatible order on the generalized support of a vector in $\mathbb F_q^n$
which allow us to describe a test set, a trial set and the set of zero
neighbours of a linear code in terms of the leader codewords.
