A Family of Quadratic Residue Codes over Z2m

摘要

A cyclic code of length n over the ring 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 math cal{C} then the cyclic shift (c_1, c_2, c_0)in math cal{C}. Quadratic residue (abbreviated QR) codes are a particularly interesting family of cyclic codes. We define such family of codes in terms of their idem potent generators and show that these codes also have many good properties which are analogous in many respects to properties of binary QR codes. Such codes constructed are self-orthogonal. And we also discuss their minimum hamming weight.