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Infinitely Many Perfect and Unitary Perfect Polynomials Over Some GF(q)

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Infinitely Many Perfect and Unitary Perfect Polynomials Over Some GF(q)

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dc.contributor.author Harbin, Mickie Sue en
dc.contributor.author Bullock, A.T. en
dc.contributor.author Beard, Jacob T. B., Jr. en
dc.date.accessioned 2010-06-03T16:16:05Z en
dc.date.available 2010-06-03T16:16:05Z en
dc.date.issued 1977-05 en
dc.identifier.uri http://hdl.handle.net/10106/2305 en
dc.description.abstract The existence is shown of infinitely many non-splitting perfect polynomials over GF(2d), GF(3d), GF(5d) for each odd integer d > 1, and over GF(2d) for each (even) integer d 1 0 (mod 3). Stronger results show that each unitary perfect polynomial over GF(q) determines an infinite equivalence class of unitary perfect polynomials over GF(q). The number SUP(q) of distinct equivalence classes of splitting unitary perfect polynomials over GF(q) is calculated for q = p and shown to be infinite for q # p. The number NSUP(q) of distinct equivalence classes of non-splitting unitary perfect polynomials over GF(q) remains undetermined, but is shown to be infinite whenever there are two relatively prime unitary perfect polynomials over GF(q) and one of them does not split. In particular NSUP(2d), NSUP(3d), and NSUP(5d) are infinite for each odd integer d > 1, and NSUP(2d) is infinite for each (even) integer d 1 0 (mod 3). Examples are given to establish NSUP(2) 33, NSUP(3) 16, and NSUP(5) 6. It is conjectured that for all primes p and odd integers d 1, NSUP(pd) is infinite. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;62 en
dc.subject Non-splitting polynomial en
dc.subject GF en
dc.subject Unitary perfect polynomials en
dc.subject Splitting polynomial en
dc.subject Many perfect polynomials en
dc.subject.lcsh Mathematics Research en
dc.subject.lcsh Polynomials en
dc.title Infinitely Many Perfect and Unitary Perfect Polynomials Over Some GF(q) en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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