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Let $S_n^\lambda$ be the set of all permutations over the multiset$\{\overbrace{1,...,1}^{\lambda},...,\overbrace{m,...,m}^\lambda\}$ where$n=m\lambda$. A frequency permutation array (FPA) of minimum distance $d$ is asubset of $S_n^\lambda$ in which every two elements have distance at least $d$.FPAs have many applications related to error correcting codes. In codingtheory, the Gilbert-Varshamov bound and the sphere-packing bound are derivedfrom the size of balls of certain radii. We propose two efficient algorithmsthat compute the ball size of frequency permutations under Chebyshev distance.Both methods extend previous known results. The first one runs in $O({2d\lambda\choose d\lambda}^{2.376}\log n)$ time and $O({2d\lambda \choosed\lambda}^{2})$ space. The second one runs in $O({2d\lambda \choosed\lambda}{d\lambda+\lambda\choose \lambda}\frac{n}{\lambda})$ time and$O({2d\lambda \choose d\lambda})$ space. For small constants $\lambda$ and $d$,both are efficient in time and use constant storage space.

Computing the Ball Size of Frequency Permutations under Chebyshev Distance