2011/12/16 by Xiongqing Tan, Tan, Xiongqing
Computer Science · Mathematics · #94B05 #Cellular Automata and Applications #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:94B05
paper · pdf · doi:10.48550/arxiv.1112.3938
arxiv created 2011/12/16 · openalex publication_date 2011/12/16 · arxiv updated 2011/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A cyclic codes of length n over the rings Z2m of integer of modulo 2m is a linear code with property that if the codeword (c0,c1,...,cn-1)∈ C then the cyclic shift (c1,c2,...,c0)∈ 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.