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

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

Published:2023-06-14 Issue:10 Volume:91 Page:3305-3319
ISSN:0925-1022
Container-title:Designs, Codes and Cryptography
language:en
Short-container-title:Des. Codes Cryptogr.

Author:

Betti Livia,Brown Jim^ORCID,Gaitan Fernando,Spear Aiyana,Varlack Japheth

Funder

Division of Mathematical Sciences

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computer Science Applications

Link

https://link.springer.com/content/pdf/10.1007/s10623-023-01258-w.pdf

Reference7 articles.

1. Chan H.H., Chua K.S., Solé P.: Quadratic iterations to $$\pi $$ associated with elliptic functions to the cubic and septic base. Trans. Am. Math. Soc. 355(4), 1505–1520 (2003).

2. Choie Y., Sharma A., Shi M.: Codes and Modular Forms: A Dictionary. World Scientific Publishing Company, Singapore (2019).

3. Chua K.S.: Codes over $${\rm GF(4)}$$ and $$\textbf{F} _2\times \textbf{F} _2$$ and Hermitian lattices over imaginary quadratic fields. Proc. Am. Math. Soc. 133(3), 661–670 (2005).

4. Ebeling W.: Lattices and Codes, 3rd edn Springer, Burgdorf (2013).

5. Neukirch J.: Algebraic Number Theory, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 322. Springer, Berlin (1999). Translated from the 1992 German original and with a note by Norbert Schappacher, With a foreword by G. Harder.

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