Five Families of Three-Weight Ternary Cyclic Codes and Their Duals

2013/08/25 by Cunsheng Ding, Ying Gao, Ding, Cunsheng +3 · 1 citation
Computer Science · Engineering · #Coding theory and cryptography #Cryptographic Implementations and Security #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1308.5373

openalex publication_date 2013/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

As a subclass of linear codes, cyclic codes have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, five families of three-weight ternary cyclic codes whose duals have two zeros are presented. The weight distributions of the five families of cyclic codes are settled. The duals of two families of the cyclic codes are optimal.

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