Construction of a class of at most three-weight linear codes and the applications
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES(2023)
摘要
Linear codes are widely studied due to their important applications in authentication codes, association schemes and strongly regular graphs, etc. In this paper, a class of at most three-weight linear codes is constructed by selecting a new defining set, then the parameters and weight distributions of codes are determined by exponential sums. Results show that almost all the linear codes we constructed are minimal and we also describe the access structures of the secret sharing schemes based on their dual. Especially, the new binary code is a two-weight projective code and based on which a strongly regular graph with new parameters is designed.
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关键词
Linear code,Defining set,Exponential sum,Weight distribution,Secret sharing scheme,Strongly regular graph
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