| Title:
|
Quasi-permutation polynomials (English) |
| Author:
|
Laohakosol, Vichian |
| Author:
|
Janphaisaeng, Suphawan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
457-488 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A quasi-permutation polynomial is a polynomial which is a bijection from one subset of a finite field onto another with the same number of elements. This is a natural generalization of the familiar permutation polynomials. Basic properties of quasi-permutation polynomials are derived. General criteria for a quasi-permutation polynomial extending the well-known Hermite's criterion for permutation polynomials as well as a number of other criteria depending on the permuted domain and range are established. Different types of quasi-permutation polynomials and the problem of counting quasi-permutation polynomials of fixed degree are investigated. (English) |
| Keyword:
|
finite fields |
| Keyword:
|
permutation polynomials |
| MSC:
|
11T55 |
| MSC:
|
12E05 |
| MSC:
|
12Y05 |
| idZBL:
|
Zbl 1224.11096 |
| idMR:
|
MR2657962 |
| . |
| Date available:
|
2010-07-20T16:52:43Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140582 |
| . |
| Reference:
|
[1] Carlitz, L., Lutz, J. A.: A characterization of permutation polynomials over a finite field.Am. Math. Mon. 85 (1978), 746-748. Zbl 0406.12011, MR 0514040, 10.2307/2321681 |
| Reference:
|
[2] Chu, W., Golomb, S. W.: Circular Tuscan-$k$ arrays from permutation binomials.J. Comb. Theory, Ser. A 97 (2002), 195-202. Zbl 1009.05032, MR 1879136, 10.1006/jcta.2001.3221 |
| Reference:
|
[3] Das, P.: The number of permutation polynomials of a given degree over a finite field.Finite Fields Appl. 8 (2002), 478-490. Zbl 1029.11066, MR 1933619 |
| Reference:
|
[4] Gantmacher, F. R.: The Theory of Matrices, Volume I.Chelsea, New York (1977). |
| Reference:
|
[5] Lidl, R., Mullen, G. L.: When does a polynomial over a finite field permute the elements of the field?.Am. Math. Mon. 95 (1988), 243-246. Zbl 0653.12010, MR 1541277, 10.2307/2323626 |
| Reference:
|
[6] Lidl, R., Mullen, G. L.: When does a polynomial over a finite field permute the elements of the field? II..Am. Math. Mon. 100 (1993), 71-74. Zbl 0777.11054, MR 1542258, 10.2307/2324822 |
| Reference:
|
[7] Lidl, R., Niederreiter, H.: Finite Fields.Addison-Wesley Reading (1983). Zbl 0554.12010, MR 0746963 |
| Reference:
|
[8] Small, C.: Permutation binomials.Int. J. Math. Math. Sci. 13 (1990), 337-342. Zbl 0702.11085, MR 1052532, 10.1155/S0161171290000497 |
| Reference:
|
[9] Wan, D., Lidl, R.: Permutation polynomials of the form $x^r f(x^{(q-1)/d})$ and their group structure.Monatsh. Math. 112 (1991), 149-163. MR 1126814, 10.1007/BF01525801 |
| Reference:
|
[10] Wan, Z.-X.: Lectures on Finite Fields and Galois Rings.World Scientific River Edge (2003). Zbl 1028.11072, MR 2008834 |
| Reference:
|
[11] Zhou, K.: A remark on linear permutation polynomials.Finite Fields Appl. 14 (2008), 532-536. MR 2401993, 10.1016/j.ffa.2007.07.002 |
| . |
