On an identity of theta functions obtained from weight enumerators of linear codes
type: Item
instance of: scholarly article
title: On an identity of theta functions obtained from weight enumerators of linear codes
zbMATH Open document ID: 0923.11072
author: Tomoaki Murayama
published in: Proceedings of the Japan Academy. Series A
publication date: 1999-06-20T00:00:00Z
review text: The following formula is proved: \[ \theta_{A^*_{n-1}}(n\tau)= F (\tau) \] for any integer \(n>1\), where on the left hand side we have the theta function of the dual \(A^*_{n-1}\) of the root lattice \(A_{n-1}\) and where \[ F(\tau)=\sum^\infty_{m=0}a_m\exp(\pi im\tau) \] with \(q=1\), \(a_j=0\) \((0<j<n-1)\), \(a_{n-1} =2n\). This generalizes a result of \textit{S. S. Rangachari} [J. Number Theory 48, 364-372 (1994; Zbl 0813.11030)].
reviewed by: Meinhard Peters
Mathematics Subject Classification ID: 11F27
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 11H06
zbMATH DE Number: 1268065
zbMATH Keywords: weight enumerators
zbMATH Keywords: linear codes
zbMATH Keywords: theta function
zbMATH Keywords: root lattice
MaRDI profile type: Publication
full work available at URL: pjaa.74.98
OpenAlex ID: W2092354607
cites work: Q4039784
cites work: Lee Polynomials of Codes and Theta Functions of Lattices
cites work: Q4040264
cites work: On a result of Ramanujan on theta functions
cites work: Q3869410
DOI: 10.3792/PJAA.74.98
description: scientific article; zbMATH DE number 1268065