2012/06/20 by Cunsheng Ding, Ding, Cunsheng · 2 citations
Computer Science · Mathematics · #Cellular Automata and Applications #Coding theory and cryptography #Cryptographic Implementations and Security #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1206.4370
openalex publication_date 2012/06/20 · arxiv created 2016/11/17 · arxiv updated 2016/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first and second kind over finite fields are employed to construct a number of classes of cyclic codes. Lower bounds on the minimum weight of some classes of the cyclic codes are developed. The minimum weights of some other classes of the codes constructed in this paper are determined. The dimensions of the codes obtained in this paper are flexible. Most of the codes presented in this paper are optimal or almost optimal in the sense that they meet some bound on linear codes. Over ninety cyclic codes of this paper should be used to update the current database of tables of best linear codes known. Among them sixty are optimal in the sense that they meet some bound on linear codes and the rest are cyclic codes having the same parameters as the best linear code in the current database maintained at http://www.codetables.de/.