Codes and Modular Forms

A Dictionary

By: Minjia Shi, Youngju Choie, Anuradha Sharma, Patrick Sole

Write A Review

eText | 20 November 2019

At a Glance

Format
ePUB

eText

$115.49

or 4 interest-free payments of $28.87 with

Instant online reading in your Booktopia eTextbook Library *

Why choose an eTextbook?

Instant Access *

Purchase and read your book immediately

Read Aloud

Listen and follow along as Bookshelf reads to you

Study Tools

Built-in study tools like highlights and more

* eTextbooks are not downloadable to your eReader or an app and can be accessed via web browsers only. You must be connected to the internet and have no technical issues with your device or browser that could prevent the eTextbook from operating.

There are connections between invariant theory and modular forms since the times of Felix Klein, in the 19th century, connections between codes and lattices since the 1960's. The aim of the book is to explore the interplay between codes and modular forms. Here modular form is understood in a wide sense (Jacobi forms, Siegel forms, Hilbert forms). Codes comprises not only linear spaces over finite fields but modules over some commutative rings. The connection between codes over finite fields and lattices has been well documented since the 1970s. Due to an avalanche of results on codes over rings since the 1990's there is a need for an update at book level.

Contents:

Codes vs Lattices: A Dictionary
Modular Forms in One Variable
Siegel Modular Forms
Jacobi Forms
Automorphic Forms over Number Fields
Construction of Self-dual Codes of Higher Lengths over ℤ_2m and Determination of Jacobi Forms
Byte Weight Enumerators of Codes and Modular Forms of Genus g
Byte Weight Enumerators of Codes over 𝔽_p and Modular Forms over a Totally Real Field

Readership: Graduate students and researchers.Codes;Self-Dual Codes;Codes Over Rings;Modular Forms;Jacobi Forms;Siegel Forms;Hilbert Forms;Theta-Series0Key Features: