  A cyclic codes of length $n$ over the rings $Z_{2^{m}}$ of integer of modulo
$2^{m}$ is a linear code with property that if the codeword
$(c_0,c_1,...,c_{n-1})\in \mathcal{C}$ then the cyclic shift
$(c_1,c_2,...,c_0)\in \mathcal{C}$. Quadratic residue codes are a particularly
interesting family of cyclic codes. We define such family of codes in terms of
their idempotent generators and show that these codes also have many good
properties which are analogous in many respects to properties of binary
quadratic residue codes. Such codes constructed are self-orthogonal. And we
also discuss their hamming weight.
