A Class of Two-Weight and Three-Weight Codes and Their Applications in Secret Sharing

2015/03/23 by Kelan Ding, Cunsheng Ding, Ding, Kelan +1 · 7 citations
Computer Science · Engineering · #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1503.06512

openalex publication_date 2015/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, a class of two-weight and three-weight linear codes over \gf(p) is constructed, and their application in secret sharing is investigated. Some of the linear codes obtained are optimal in the sense that they meet certain bounds on linear codes. These codes have applications also in authentication codes, association schemes, and strongly regular graphs, in addition to their applications in consumer electronics, communication and data storage systems.

Citations

• How to share a secret

Cited by

• r-Minimal Poset Codes
• On the Hamming Weight Functions of Linear Codes
• Several classes of three-weight or four-weight linear codes
• Several classes of p-ary linear codes with few-weights derived from Weil sums
• On a class of quasi-Hermitian surfaces in even characteristic
• Several new classes of self-orthogonal minimal linear codes violating the Ashikhmin-Barg condition
• Minimal Linear Codes Violating the Ashikhmin-Barg Condition from Arbitrary Projective Linear Codes

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• A Class of Two-Weight and Three-Weight Linear Codes and Their Duals
• A class of three-weight and five-weight linear codes
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• Weight distributions of two classes of linear codes
• A Class of Linear Codes with a Few Weights