Title :
A Family of Quadratic Residue Codes over Z2m
Author_Institution :
Dept. of Math., Jinan Univ., Guangzhou, China
Abstract :
A cyclic code of length n over the ring Z2m of integer of modulo 2m is a linear code with property that if the codeword (c0, c1, cn-1) in ∈ C then the cyclic shift (c1, c2, c0) in math ∈ 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.
Keywords :
codes; binary QR codes; codeword; cyclic code; cyclic shift; idempotent generators; minimum hamming weight; quadratic residue codes; Educational institutions; Generators; Hamming weight; Linear codes; Polynomials; Vectors; Generators of $Z_{2^{m}}$-cyclic codes; idempotents of $Z_{2^{m}}$-cyclic codes; quadratic residue codes; self-orthogonal codes;
Conference_Titel :
Emerging Intelligent Data and Web Technologies (EIDWT), 2013 Fourth International Conference on
Conference_Location :
Xi´an
Print_ISBN :
978-1-4799-2140-9
DOI :
10.1109/EIDWT.2013.46
