Computing the Ball Size of Frequency Permutations under Chebyshev Distance

Min-Zheng Shieh*, Shi-Chun Tsai

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations

Abstract

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.

Original languageEnglish
Title of host publication2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Pages2100-2104
Number of pages5
DOIs
StatePublished - 26 Oct 2011
Event2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation
Duration: 31 Jul 20115 Aug 2011

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8104

Conference

Conference2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
CountryRussian Federation
CitySt. Petersburg
Period31/07/115/08/11

Fingerprint Dive into the research topics of 'Computing the Ball Size of Frequency Permutations under Chebyshev Distance'. Together they form a unique fingerprint.

Cite this