2015•IEEE Communications LettersRequires access

Binary Linear Codes With Few Weights

Yanfeng Qi, Chunming Tang, Dongmei Huang

Abstract

Linear codes can be applied in secret sharing, authentication codes, association schemes, and strongly regular graphs. This letter generalizes the construction of linear codes by Ding et al. [9], uses more flexible construction method, and presents linear codes with few weights. These codes contain two-weight linear codes, one-weight linear codes, and three-weight linear codes. These codes contain some optimal codes meeting certain bound on linear codes.

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Key concepts: Linear code, Block code, Expander code, Reed–Muller code, Luby transform code, Raptor code, Tornado code, Concatenated error correction code