Computing the ball size of frequency permutations under chebyshev distance
Min-Zheng Shieh, Shi‐Chun Tsai · 2011
Let Sλnbe the set of all permutations over the multiset {1,...,1,...,m,...,m} where n = mλ. A frequency permutation array (FPA) of minimum distance d is a subset of Sλnin 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((2dλdλ)2.376log n) time and O ((2dλdλ)2)space. The second one runs in O ((2dλdλ)((dλ+λ)/λ)n/λ) time and O ((2dλdλ)) space. For small constants λ and d, both are efficient in time and use constant storage space.