Title: Byte weight enumerators of codes over 𝔽_p and modular forms over a totally real field

Authors: Anuradha Sharma; Amit K. Sharma

Addresses: Department of Mathematics, IIIT Delhi, New Delhi, India ' Department of Mathematics, IIT Delhi, New Delhi, India

Abstract: In this paper, we obtain Jacobi forms over k_p from byte weight enumerators of self-dual codes over 𝔽_p, where p is an odd prime, k_p is the totally real field of the pth cyclotomic field and 𝔽_p is the finite field of order p. We also determine Siegel modular forms of genus g (g ≥ 1 is an integer) over k_p by substituting certain theta series into byte weight enumerators in genus g of self-dual codes over 𝔽_p for all p ∈ 𝔓, where the set 𝔓 consists of all those odd primes p for which the ring of algebraic integers of k_p 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.

Keywords: algebraic integers; lattices; theta series.

DOI: 10.1504/IJICOT.2017.086905

International Journal of Information and Coding Theory, 2017 Vol.4 No.4, pp.237 - 257

Received: 14 Dec 2016
Accepted: 27 Dec 2016
Published online: 02 Oct 2017 *

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