On permutation polynomials over finite fields
A polynomial f over a finite field F is called a permutation polynomial if the mapping F→F defined by f is one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a polynomial which are necessary and sufficient f...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171287000644 |
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| _version_ | 1832564365849526272 |
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| author | R. A. Mollin C. Small |
| author_facet | R. A. Mollin C. Small |
| author_sort | R. A. Mollin |
| collection | DOAJ |
| description | A polynomial f over a finite field F is called a permutation polynomial if the mapping F→F defined by f is one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a polynomial which are necessary and sufficient for it to represent a permutation. We also give some results bearing on a conjecture of Carlitz which says essentially that for any even integer m, the cardinality of finite fields admitting permutation polynomials of degree m is bounded. |
| format | Article |
| id | doaj-art-e0d499142d61437883aa0d29275ad253 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e0d499142d61437883aa0d29275ad2532025-02-03T01:11:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110353554310.1155/S0161171287000644On permutation polynomials over finite fieldsR. A. Mollin0C. Small1Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, CanadaDepartment of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4, CanadaA polynomial f over a finite field F is called a permutation polynomial if the mapping F→F defined by f is one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a polynomial which are necessary and sufficient for it to represent a permutation. We also give some results bearing on a conjecture of Carlitz which says essentially that for any even integer m, the cardinality of finite fields admitting permutation polynomials of degree m is bounded.http://dx.doi.org/10.1155/S0161171287000644polynomialsirreducibilityfactorizationdistribution of values. |
| spellingShingle | R. A. Mollin C. Small On permutation polynomials over finite fields International Journal of Mathematics and Mathematical Sciences polynomials irreducibility factorization distribution of values. |
| title | On permutation polynomials over finite fields |
| title_full | On permutation polynomials over finite fields |
| title_fullStr | On permutation polynomials over finite fields |
| title_full_unstemmed | On permutation polynomials over finite fields |
| title_short | On permutation polynomials over finite fields |
| title_sort | on permutation polynomials over finite fields |
| topic | polynomials irreducibility factorization distribution of values. |
| url | http://dx.doi.org/10.1155/S0161171287000644 |
| work_keys_str_mv | AT ramollin onpermutationpolynomialsoverfinitefields AT csmall onpermutationpolynomialsoverfinitefields |