On the weak order ideal associated to linear codes
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 allows to describe a test set, a trial set and the set of zero neighbours of a linear code in terms of the leader codewords.
In the present paper, we study the Sp-module structure of the cokernel of the Johnson homomorphism of the mapping class groups of surfaces. We detect the Sp-irreducible components with highest weight [1^k] (and [k]) in the cokernel. We also show that the multiplicities of them is equal to one.