Codes and Siegel modular forms
Discrete Mathematics
The Invariants of the Clifford Groups
Designs, Codes and Cryptography
Type II codes, even unimodular lattices, and invariant rings
IEEE Transactions on Information Theory
Complete weight enumerators of generalized doubly-even self-dual codes
Finite Fields and Their Applications
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We consider type II codes over finite rings$$\mathbb{Z}/2k\mathbb{Z} $$. It is well-known that their gth complete weight enumerator polynomials are invariant under the action of a certain finite subgroup of$$GL((2k)^g,\mathbb{C})$$, which we denote Hk,g. We show that the invariant ring with respect to Hk,g is generated by such polynomials. This is carried out by using some closely related results concerning theta series and Siegel modular forms with respect to$$Sp(g,\mathbb{Z})$$.