zbMATH — the first resource for mathematics

Constructing permutations of finite fields via linear translators. (English) Zbl 1241.11136
Summary: Methods for constructing large families of permutation polynomials of finite fields are introduced. For some of these permutations the cycle structure and the inverse mapping are determined. The results are applied to lift minimal blocking sets of \(\text{PG}(2,q)\) to those of \(\text{PG}(2,q^n)\).

11T06 Polynomials over finite fields
51E21 Blocking sets, ovals, \(k\)-arcs
Full Text: DOI arXiv
[1] Ball, S., The number of directions determined by a function over a finite field, J. combin. theory ser. A, 104, 341-350, (2003) · Zbl 1045.51004
[2] Blokhuis, A.; Ball, S.; Brouwer, A.E.; Storme, L.; Szőnyi, T., On the number of slopes of the graph of a function defined on a finite field, J. combin. theory ser. A, 86, 187-196, (1999) · Zbl 0945.51002
[3] Blokhuis, A.; Brouwer, A.E.; Szőnyi, T., The number of directions determined by a function f on a finite field, J. combin. theory ser. A, 70, 349-353, (1995) · Zbl 0823.51013
[4] Charpin, P.; Kyureghyan, G., Monomial functions with linear structure and permutation polynomials, (), 99-111 · Zbl 1221.12008
[5] Charpin, P.; Kyureghyan, G., When does \(F(X) + \gamma \operatorname{Tr}(H(X))\) permute \(F_{p^n}\)?, Finite fields appl., 15, 5, 615-632, (2009) · Zbl 1229.11153
[6] Charpin, P.; Kyureghyan, G., On a class of permutation polynomials over \(F_{2^n}\), (), 368-376 · Zbl 1180.11038
[7] Evans, R.J.; Greene, J.; Niederreiter, H., Linearized polynomials and permutation polynomials of finite fields, Michigan math. J., 39, 3, 405-413, (1992) · Zbl 0777.11052
[8] Lai, X., Additive and linear structures of cryptographic functions, (), 75-85 · Zbl 0939.94508
[9] J.E. Marcos, Specific permutation polynomials over finite fields, Finite Fields Appl. (2010), in press.
[10] Niederreiter, H.; Robinson, K.H., Complete mappings of finite fields, J. aust. math. soc., 33, 197-212, (1982) · Zbl 0495.12018
[11] Rédei, L., Lückenhafte polynome über endlichen Körpern, (1970), Birkhäuser Verlag Basel · Zbl 0321.12028
[12] Szőnyi, T.; Gács, A.; Weiner, Zs., On the spectrum of minimal blocking sets in \(\operatorname{PG}(2, q)\), J. geom., 76, 256-281, (2003) · Zbl 1032.51011
[13] Zieve, M.E., Classes of permutation polynomials based on cyclotomy and an additive analogue · Zbl 1261.11081
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.