The average of joint weight enumerators

The Joint Weight Enumerators and Siegel Modular Forms

The weight enumerator of a binary doubly even self-dual code is an isobaric polynomial in the two generators of the ring of invariants of a certain group of order 192. The aim of this note is to study the ring of coefficients of that polynomial, both for standard and joint weight enumerators.

Quantum Weight Enumerators

In a recent paper, Shor and Laflamme define two “weight enumerators” for quantum error-correcting codes, connected by a MacWilliams transform, and use them to give a linear-programming bound for quantum codes. We introduce two new enumerators which, while much less powerful at producing bounds, are useful tools nonetheless. The new enumerators are connected by a much simpler duality transform, ...

Ring of the weight enumerators of dn

We show that the ring of the weight enumerators of a self-dual doubly even code dn in arbitrary genus is finitely generated. Indeed enough elements to generate it are given. The latter result is applied to obtain a minimal set of generators of the ring in genus two.

Extended and generalized weight enumerators

This paper gives a survey on extended and generalized weight enumerators of a linear code and the Tutte polynomial of the matroid of the code [16]. Furthermore ongoing research is reported on the coset leader and list weight enumerator and its extensions using the derived code and its arrangement of hyperplanes.

Weight enumerators of self-orthogonal codes