2024/07/10 by Gaofei Wu, Zhuohui You, Wu, Gaofei +5 · 1 citation
Computer Science · Engineering · Medicine · #Cancer Mechanisms and Therapy #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2407.07332
openalex publication_date 2024/07/10 · openalex created_date 2024/07/13 · openalex updated_date 2026/07/28
Cyclic codes are a subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics due to their efficient encoding and decoding algorithms. Let α be a generator of \mathbbF3m^*, where m is a positive integer. Denote by C(i1,i2,⋯, it) the cyclic code with generator polynomial mαi1(x)mαi2(x)⋯ mαit(x), where mαi(x) is the minimal polynomial of αi over \mathbbF3. In this paper, by analyzing the solutions of certain equations over finite fields, we present four classes of optimal ternary cyclic codes C(0,1,e) and C(1,e,s) with parameters [3m-1,3m-(3m)/(2)-2,4], where s=(3m-1)/(2). In addition, by determining the solutions of certain equations and analyzing the irreducible factors of certain polynomials over \mathbbF3m, we present four classes of optimal ternary cyclic codes C(2,e) and C(1,e) with parameters [3m-1,3m-2m-1,4]. We show that our new optimal cyclic codes are inequivalent to the known ones.