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- W2950883609 abstract "Let $S_n^lambda$ be the set of all permutations over the multiset ${overbrace{1,...,1}^{lambda},...,overbrace{m,...,m}^lambda}$ where $n=mlambda$. A frequency permutation array (FPA) of minimum distance $d$ is a subset of $S_n^lambda$ in which every two elements have distance at least $d$. FPAs have many applications related to error correcting codes. In coding theory, the Gilbert-Varshamov bound and the sphere-packing bound are derived from the size of balls of certain radii. We propose two efficient algorithms that compute the ball size of frequency permutations under Chebyshev distance. Both methods extend previous known results. The first one runs in $O({2dlambda choose dlambda}^{2.376}log n)$ time and $O({2dlambda choose dlambda}^{2})$ space. The second one runs in $O({2dlambda choose dlambda}{dlambda+lambdachoose lambda}frac{n}{lambda})$ time and $O({2dlambda choose dlambda})$ space. For small constants $lambda$ and $d$, both are efficient in time and use constant storage space." @default.
- W2950883609 created "2019-06-27" @default.
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- W2950883609 date "2011-02-14" @default.
- W2950883609 modified "2023-10-16" @default.
- W2950883609 title "Computing the Ball Size of Frequency Permutations under Chebyshev Distance" @default.
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