Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2009; 46(1): 13-30

Printed January 1, 2009

Copyright © The Korean Mathematical Society.

Quadratic residue codes over ${\mathbb Z}_9$

Bijan Taeri

Isfahan University of Technology

Abstract

A subset of $n$ tuples of elements of ${\mathbb Z}_9$ is said to be a code over ${\mathbb Z}_9$ if it is a ${\mathbb Z}_9$-module. In this paper we consider an special family of cyclic codes over ${\mathbb Z}_9$, namely quadratic residue codes. We define these codes in term of their idempotent generators and show that these codes also have many good properties which are analogous in many respects to properties of quadratic residue codes over finite fields.

Keywords: cyclic codes, quadratic residue codes, extended codes, automorphism group of a code

MSC numbers: 11T71, 94B05, 94B15, 94B99