Jacobi forms over totally real fields and type II codes over Galois rings \(\operatorname{GR}(2^{m},f)\).
In this paper, the authors study type II codes over Galois rings and their weight enumerators over an invariant polynomial ring of generalized Clifford-Weil group, as it has been done for codes over \(\mathbb{F}_{2^2}\). They use an algebra homomorphism to give a correspondance between Jacobi forms over totally real field and this invariant polynomial ring where weight enumerators belong. As an example, authors illustrate their results with a complete list of type II codes of length 4 over Galois ring of cardinality 16 and characteristic 4. Citations are well used and results are well presented highlighting the interest of the topic, type II codes over Galois rings of characteristic a power of 2 and their link with Jacobi modular forms.
scientific article; zbMATH DE number 2082041
scientific article