Linear Codes With Two or Three Weights From Weakly Regular Bent Functions

2016/01/18 by Chunming Tang, Nian Li, Yanfeng Qi +2 · 17 citations
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Cooperative Communication and Network Coding

paper · doi:10.1109/tit.2016.2518678

Abstract

Linear codes with a few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of constructing two-weight and three-weight linear codes of Ding et al. and Zhou et al. to general weakly regular bent functions and determines the weight distributions of these linear codes. It solves an open problem proposed by Ding et al. Furthermore, this paper constructs new linear codes with two or three weights and presents their weight distributions. They contain some optimal codes meeting certain bound on linear codes.

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• New results on vectorial dual-bent functions and partial difference sets
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• Some punctured codes of several families of binary linear codes
• Random Matrices from Linear Codes and Wigner's Semicircle Law II
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• Complete weight enumerators for several classes of two-weight and three-weight linear codes
• Two-weight and three-weight linear codes based on Weil sums
• Linear Codes from Two Weakly Regular Plateaued Balanced Functions. [europepmc]
• Linear Codes Constructed from Two Weakly Regular Plateaued Functions with Index ( p - 1)/2. [europepmc]

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• Linear codes with two or three weights from weakly regular bent functions
• Linear Codes with Two or Three Weights From Quadratic Bent Functions
• Linear codes with few weights from non-weakly regular plateaued functions
• A Class of Two-Weight and Three-Weight Linear Codes and Their Duals
• A Class of Linear Codes With Three Weights