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- W4287062904 abstract "We study sequences of linear or affine codes with uniform weight spectrum, i.e., a part of codewords with any fixed weight tends to zero. It is proved that a sequence of linear codes has a uniform weight spectrum if the number of vectors from codes with weight $1$ grows to infinity. We find an example of a sequence of linear codes such that the dimension of the code is the half of the codelength but it has not a uniform weight spectrum. This example generates eigenfunctions of the Fourier transform with minimal support and partial covering sets. Moreover, we generalize some MacWilliams-type identity. Keywords: weight distribution of code, dual code, MacWilliams identity, Fourier transform, partial covering array" @default.
- W4287062904 created "2022-07-25" @default.
- W4287062904 creator A5045171871 @default.
- W4287062904 date "2021-07-30" @default.
- W4287062904 modified "2023-09-24" @default.
- W4287062904 title "On weight spectrum of linear codes" @default.
- W4287062904 doi "https://doi.org/10.48550/arxiv.2107.14576" @default.
- W4287062904 hasPublicationYear "2021" @default.
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