Hilbert modular forms and codes over \(\mathbb{F}_{p^2}\)

DOI10.1016/j.ffa.2020.101731zbMath1456.11077OpenAlexW3047541664MaRDI QIDQ1994943

Felice Manganiello, Beren Gunsolus, Jeremy Lilly, Jim L. Brown

Publication date: 18 February 2021

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2020.101731

zbMATH Keywords

theta serieslatticescoding theory

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Bounds on codes (94B65) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41) Relations with coding theory (11H71)

Cites Work

• Codes over rings of size \(p^2\) and lattices over imaginary quadratic fields
• Codes over rings, complex lattices and Hermitian modular forms
• Codes over \(\mathbb F_4\), Jacobi forms and Hilbert-Siegel modular forms over \(\mathbb Q(\sqrt 5)\)
• Jacobi forms over totally real fields and type II codes over Galois rings \(\operatorname{GR}(2^{m},f)\).
• Jacobi forms over totally real fields and codes over \(\mathbb F_p\)
• A generalization of the Lee distance and error correcting codes
• Codes over \(\mathbb{Z}_{2m}\) and Jacobi forms of genus \(n\)
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