A Family of Five-Weight Cyclic Codes and Their Weight Enumerators

2013/02/05 by Zhengchun Zhou, Cunsheng Ding, Zhou, Zhengchun +5 · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1302.0952

openalex publication_date 2013/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, a family of p-ary cyclic codes whose duals have three zeros are proposed. The weight distribution of this family of cyclic codes is determined. It turns out that the proposed cyclic codes have five nonzero weights.

Cited by

• A note on the five valued conjectures of Johansen and Helleseth and zeta functions

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