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\iteman{io-port 06121508}
\itemau{Carmelo, Emerson L.Monte}
\itemti{Covering codes and extremal problems from invariant sets under permutations.}
\itemso{Discrete Math. 313, No. 3, 249-257 (2013).}
\itemab
Summary: Let $c_{q}(n,R)$ denote the minimum cardinality of a subset $H$ in $\Bbb F^n_q$ such that every word in this space differs in at most $R$ coordinates from a scalar multiple of a vector in $H$, where $q$ is a prime power. In order to explore symmetries of such coverings, a few properties of invariant sets under certain permutations are investigated. New classes of upper bounds on $c_{q}(n,R)$ are obtained, extending previous results. Let $K_{q}(n,R)$ denote the minimum cardinality of an $R$-covering code in the $n$-dimensional space over an alphabet with $q$ symbols. As another application, a very-known upper bound on $K_{q}(n,R)$ is improved under certain conditions. Moreover, two extremal problems are discussed by using tools from graph theory.
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\itemut{invariant set; permutation; covering; bounds on code; independent set; matching}
\itemli{doi:10.1016/j.disc.2012.10.002}
\end