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- W2895029824 abstract "We say a subspace $U$ of ${mathbb{F}_q^n}$ is cyclically covering if the union of the cyclic shifts of $U$ is equal to $mathbb{F}_q^n$. We investigate the problem of determining the minimum possible dimension of a cyclically covering subspace of $mathbb{F}_q^n$. (This is a natural generalisation of a problem posed in 1991 by the first author.) We prove several upper and lower bounds, and for each fixed $q$, we answer the question completely for infinitely many values of $n$ (which take the form of certain geometric series). We also consider the analogous problem for general representations of groups. We use arguments from combinatorics, representation theory and Galois theory." @default.
- W2895029824 created "2018-10-12" @default.
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- W2895029824 date "2018-10-08" @default.
- W2895029824 modified "2023-09-26" @default.
- W2895029824 title "Smallest cyclically covering subspaces of $mathbb{F}_q^n$" @default.
- W2895029824 hasPublicationYear "2018" @default.
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