Codes over F4, Jacobi forms and Hilbert–Siegel modular forms over Q(5)

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Abstract

We study codes over a finite field F4. We relate self-dual codes over F4 to real 5-modular lattices and to self-dual codes over F2 via a Gray map. We construct Jacobi forms over Q(5) from the complete weight enumerators of self-dual codes over F4. Furthermore, we relate Hilbert–Siegel forms to the joint weight enumerators of self-dual codes over F4.

Keywords

Self-dual codes
Integral lattices
Jacobi forms
Hilbert modular forms
Hilbert–Siegel modular forms over Q(5)

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