Hamming weight enumerators of multi-twisted codes with at most two non-zero constituents |
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| Affiliation: | 1. Key Laboratory of Intelligent Computing Signal Processing, Ministry of Education, School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, China;2. School of Mathematical Sciences, Anhui University, Hefei, 230601, China;3. Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey;4. I2M, Aix Marseille Univ., Centrale Marseille, CNRS, Marseille, France |
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| Abstract: | In this paper, we explicitly determine Hamming weight enumerators of several classes of multi-twisted codes over finite fields with at most two non-zero constituents, where each non-zero constituent has dimension 1. Among these classes of multi-twisted codes, we further identify two classes of optimal equidistant linear codes that have nice connections with the theory of combinatorial designs and several other classes of minimal linear codes that are useful in constructing secret sharing schemes with nice access structures. We also illustrate our results with some examples. |
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| Keywords: | Gauss sums Hamming weight distributions Optimal equidistant codes |
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