# QUADRATIC RESIDUE CODES OVER ℤ9

• Taeri, Bijan (DEPARTMENT OF MATHEMATICAL SCIENCES ISFAHAN UNIVERSITY OF TECHNOLOGY, INSTITUTE FOR STUDIES IN THEORETICAL PHYSICS AND MATHEMATICS)
• Published : 2009.01.31

#### 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.

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