Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey)

Eiichi Bannai

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 3, page 763-782
  • ISSN: 0373-0956

Abstract

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Modular invariance property of association schemes is recalled in connection with our joint work with François Jaeger. Then we survey codes over F 2 discussing how codes, through their (various kinds of) weight enumerators, are related to (various kinds of) modular forms through polynomial invariants of certain finite group actions and theta series. Recently, not only codes over an arbitrary finite field but also codes over finite rings and finite abelian groups are considered and have been studied extensively. We show how the determination of the solutions of the modular invariance property of finite abelian groups (our joint work with Jaeger) is used to define the concept of Type II codes over arbitrary finite abelian groups. As an example of the usefulness of such Type II codes, we give an application to hermitian modular forms.

How to cite

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Bannai, Eiichi. "Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey)." Annales de l'institut Fourier 49.3 (1999): 763-782. <http://eudml.org/doc/75361>.

@article{Bannai1999,
abstract = {Modular invariance property of association schemes is recalled in connection with our joint work with François Jaeger. Then we survey codes over $F_2$ discussing how codes, through their (various kinds of) weight enumerators, are related to (various kinds of) modular forms through polynomial invariants of certain finite group actions and theta series. Recently, not only codes over an arbitrary finite field but also codes over finite rings and finite abelian groups are considered and have been studied extensively. We show how the determination of the solutions of the modular invariance property of finite abelian groups (our joint work with Jaeger) is used to define the concept of Type II codes over arbitrary finite abelian groups. As an example of the usefulness of such Type II codes, we give an application to hermitian modular forms.},
author = {Bannai, Eiichi},
journal = {Annales de l'institut Fourier},
keywords = {modular invariance; association scheme; spin model; code over finite ring; type II code; hermitian modular form},
language = {eng},
number = {3},
pages = {763-782},
publisher = {Association des Annales de l'Institut Fourier},
title = {Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey)},
url = {http://eudml.org/doc/75361},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Bannai, Eiichi
TI - Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey)
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 3
SP - 763
EP - 782
AB - Modular invariance property of association schemes is recalled in connection with our joint work with François Jaeger. Then we survey codes over $F_2$ discussing how codes, through their (various kinds of) weight enumerators, are related to (various kinds of) modular forms through polynomial invariants of certain finite group actions and theta series. Recently, not only codes over an arbitrary finite field but also codes over finite rings and finite abelian groups are considered and have been studied extensively. We show how the determination of the solutions of the modular invariance property of finite abelian groups (our joint work with Jaeger) is used to define the concept of Type II codes over arbitrary finite abelian groups. As an example of the usefulness of such Type II codes, we give an application to hermitian modular forms.
LA - eng
KW - modular invariance; association scheme; spin model; code over finite ring; type II code; hermitian modular form
UR - http://eudml.org/doc/75361
ER -

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