Constructing Permutation Arrays of Known Distance

dc.contributor.advisorSudborough, Ivan Hal
dc.contributor.advisorBereg, Sergey
dc.contributor.advisorChiu, Yun
dc.contributor.committeeMemberRaichel, Benjamin
dc.contributor.committeeMemberDu, Ding-Zhu
dc.contributor.committeeMemberChandrasekaran, R.
dc.creatorMalouf, Brian D.
dc.creator.orcid0000-0003-2795-9265
dc.date.accessioned2023-09-27T16:08:15Z
dc.date.available2023-09-27T16:08:15Z
dc.date.created2023-05
dc.date.issuedMay 2023
dc.date.submittedMay 2023
dc.date.updated2023-09-27T16:08:16Z
dc.description.abstractA permutation array (PA) is a set of permutations on n symbols. A PA is said to have distance d (under some metric) if every pair of distinct permutations in the array has distance at least d. Commonly used distance metrics include Hamming distance and Chebyshev distance. PAs of a known distance can be used to construct error-correcting codes and have applications in communication over noisy channels. Let M (n, d) represent the maximum size of a permutation array on n symbols with pairwise Hamming distance d. Let P (n, d) represent the maximum size of a permutation array on n symbols with pairwise Chebyshev distance d. Exact values of M (n, d) and P (n, d) are unknown for most values n and d with the exception of some special cases. While combinatorial upper and lower bounds exist for both M (n, d) and P (n, d), these can often be improved through empirical techniques. We present several such techniques to construct PAs under the Hamming and Chebyshev distance metrics, resulting in improved bounds for both M (n, d) and P (n, d).
dc.format.mimetypeapplication/pdf
dc.identifier.uri
dc.identifier.urihttps://hdl.handle.net/10735.1/9899
dc.language.isoEnglish
dc.subjectComputer Science
dc.titleConstructing Permutation Arrays of Known Distance
dc.typeThesis
dc.type.materialtext
thesis.degree.collegeSchool of Engineering and Computer Science
thesis.degree.departmentComputer Science
thesis.degree.grantorThe University of Texas at Dallas
thesis.degree.nameDoctor of Philosophy

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