-adic estimates for exponential sums and the theorem of Chevalley-Warning
Pairs of Bilinear and Quadratic Equations in a Finite Field.
Partitions quadratiques et cyclotomie
p-dimensionale Vektoren modulo p. I. Zyklische Theorie.
p-dimensionale Vektoren modulo p. II.
Period of a linear recurrence
Period polynomials and Gauss sums for finite fields
Periodic harmonic functions on lattices and points count in positive characteristic
This survey deals with pluri-periodic harmonic functions on lattices with values in a field of positive characteristic. We mention, as a motivation, the game “Lights Out” following the work of Sutner [20], Goldwasser- Klostermeyer-Ware [5], Barua-Ramakrishnan-Sarkar [2, 19], Hunzikel-Machiavello-Park [12] e.a.; see also [22, 23] for a more detailed account. Our approach uses harmonic analysis and algebraic geometry over a field of positive characteristic.
Permutation binomials.
Permutation matrices and matrix equivalence over a finite field.
Permutation polynomials in several variables over finite fields
Permutation Polynomials of the Form x... f (x...) and Their Group Structure.
Permutations with coefficients in a subfield
Poids des duaux des codes BCH de distance prescrite et sommes exponentielles
Soit un entier pair. On considère un code BCH binaire de longueur et de distance prescrite avec . Le poids d’un mot non nul du dual de peut s’exprimer en fonction d’une somme exponentielle. Nous montrerons que cette somme n’atteint pas la borne de Weil et nous proposerons une amélioration de celle-ci. En conséquence, nous obtiendrons une amélioration de la borne de Carlitz-Uchiyama sur le poids des mots du dual de .
Poids des duaux des codes BCH de distance prescrite et sommes exponentielles
Point Sets and Sequences with Small Discrepancy.
Polynômes de ayant un diviseur de degré donné
Polynômes irréductibles primitifs à coefficients dans un corps fini
Polynômes singuliers à plusieurs variables sur un corps fini et congruences modulo p²
Polynomial Automorphisms Over Finite Fields
It is shown that the invertible polynomial maps over a finite field Fq , if looked at as bijections Fn,q −→ Fn,q , give all possible bijections in the case q = 2, or q = p^r where p > 2. In the case q = 2^r where r > 1 it is shown that the tame subgroup of the invertible polynomial maps gives only the even bijections, i.e. only half the bijections. As a consequence it is shown that a set S ⊂ Fn,q can be a zero set of a coordinate if and only if #S = q^(n−1).