TY - GEN

T1 - Computing the Ball Size of Frequency Permutations under Chebyshev Distance

AU - Shieh, Min-Zheng

AU - Tsai, Shi-Chun

PY - 2011

Y1 - 2011

N2 - Let Sλn be the set of all permutations over the multiset {1,⋯,1,λ ⋯,m,⋯,m λ} where n = mλ. A frequency permutation array (FPA) of minimum distance d is a subset of Sλn 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 ((2dλ dλ)2.376log n) time and O ((2dλ dλ)2) space. The second one runs in O ((2dλ dλ) (dλ+λ λ)n/λ) time and O ((2dλ dλ)) space. For small constants λ and d, both are efficient in time and use constant storage space.

AB - Let Sλn be the set of all permutations over the multiset {1,⋯,1,λ ⋯,m,⋯,m λ} where n = mλ. A frequency permutation array (FPA) of minimum distance d is a subset of Sλn 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 ((2dλ dλ)2.376log n) time and O ((2dλ dλ)2) space. The second one runs in O ((2dλ dλ) (dλ+λ λ)n/λ) time and O ((2dλ dλ)) space. For small constants λ and d, both are efficient in time and use constant storage space.

UR - http://www.scopus.com/inward/record.url?scp=80054817994&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2011.6033927

DO - 10.1109/ISIT.2011.6033927

M3 - Conference contribution

AN - SCOPUS:80054817994

SN - 9781457705953

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2100

EP - 2104

BT - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

T2 - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

Y2 - 31 July 2011 through 5 August 2011

ER -