Linear codes with few weights from weakly regular plateaued functions |
| |
Institution: | 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 |
| |
Abstract: | Linear codes with few nonzero weights have wide applications in secret sharing, authentication codes, association schemes and strongly regular graphs. Recently, Wu et al. (2020) obtained some few-weighted linear codes by employing bent functions. In this paper, inspired by Wu et al. and some pioneers' ideas, we use a kind of functions, namely, general weakly regular plateaued functions, to define the defining sets of linear codes. Then, by utilizing some cyclotomic techniques, we construct some linear codes with few weights and obtain their weight distributions. Notably, some of the obtained codes are almost optimal with respect to the Griesmer bound. Finally, we observe that our newly constructed codes are minimal for almost all cases. |
| |
Keywords: | Linear code Weakly regular plateaued function Weight distribution Exponential sum |
本文献已被 ScienceDirect 等数据库收录! |
|