Lattices in real quadratic fields and associated theta series arising from codes over \({\mathbb{F}}_4\) and \({\mathbb{F}}_2 \times {\mathbb{F}}_2\)

DOI10.1007/s10623-023-01258-wOpenAlexW4380609544MaRDI QIDQ6050262

Japheth Varlack, Fernando Gaitan, Jim L. Brown, Aiyana Spear, Livia Betti

Publication date: 12 October 2023

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10623-023-01258-w

zbMATH Keywords

theta seriesreal quadratic fieldslatticescoding theory

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Theta series; Weil representation; theta correspondences (11F27) Relations with coding theory (11H71)

Cites Work

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• Lattices and Codes
• Quadratic iterations to ${\pi }$ associated with elliptic functions to the cubic and septic base
• Codes over $\mathbf {GF\pmb (4\pmb )}$ and $\mathbf {F}_2 \times \mathbf {F}_2$ and Hermitian lattices over imaginary quadratic fields
• Codes and Modular Forms
• Codes over rings of size four, Hermitian lattices, and corresponding theta functions

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