Quadratic residue codes over the integers modulo q^m - A Preliminary Report
by
Pramod Kanwar
Truman State University

Let p be an odd prime and q be a prime ( =/= p) which is a quadratic residue modulo p. Let x^p-1=(x-1)g_q(x)h_q(x) over Z_q[x]. The cyclic Z_q-codes of length p generated by g_q(x), (x-1)g_q(x), h_q(x), (x-1)h_q(x) are called quadratic residue Z_q-codes. The purpose of this paper is to generalize this idea to codes over Z_q^m. Writing x^p-1=(x-1)g(x)h(x) over Z_q^m[x], the quadratic residue Z_q^m-codes of length p are defined as the cyclic Z_q^m-codes of length p generated by g(x), (x-1)g(x), h(x), (x-1)h(x). It is shown that these codes have properties similar to the quadratic re sidue Z_q-codes of length p. The extended quadratic residue Z_q^m-codes are defined and their properties are also studied.

Date received: February 19, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabw-82.