J. Korean Math. Soc. 2009; 46(1): 13-30
Printed January 1, 2009
Copyright © The Korean Mathematical Society.
Bijan Taeri
Isfahan University of Technology
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
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