Constructing few-weight linear codes and strongly regular graphs |
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Affiliation: | 1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, NanJing 211106, China;2. Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), MIIT, NanJing 211106, China |
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Abstract: | Linear codes with few weights have applications in data storage systems, secret sharing schemes, graph theory and so on. In this paper, we construct a class of few-weight linear codes by choosing defining sets from cyclotomic classes and we also establish few-weight linear codes by employing weakly regular bent functions. Notably, we get some codes that are minimal and we also obtain a class of two-weight optimal punctured codes with respect to the Griesmer bound. Finally, we get a class of strongly regular graphs with new parameters by using the obtained two-weight linear codes. |
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Keywords: | Linear code Weakly regular bent function Weight distribution Minimal code Strongly regular graph |
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