Byte weight enumerators of codes over 𝔽p and modular forms over a totally real field. (2017)

• Record Type: Journal Article
• Authors: Sharma, Anuradha; Sharma, Amit K.
• Is Part Of: International journal of information and coding theory. Volume 4:Number 4(2017)
• Page Start: 237
• Page End: 257
• Publication Date: 2017
• Subjects: algebraic integers -- lattices -- theta series; Coding theory -- Periodicals; Information theory -- Periodicals; 003.54
• Languages: English
• ISSNs: 1753-7703

Abstract

In this paper, we obtain Jacobi forms over kp from byte weight enumerators of self-dual codes over 𝔽p, where p is an odd prime, kp is the totally real field of the pth cyclotomic field and 𝔽p is the finite field of order p. We also determine Siegel modular forms of genus g (g ≥ 1 is an integer) over kp by substituting certain theta series into byte weight enumerators in genus g of self-dual codes over 𝔽p for all p ∈ 𝔓, where the set 𝔓 consists of all those odd primes p for which the ring of algebraic integers of kp is a Euclidean domain. Further, we define some partial Epstein zeta functions and derive their functional equation using the Mellin transform of the theta series.