Deficiency and Ambiguity of Low Degree Permutation Polynomials
Ommkaltoum Omar · 2016
In this thesis, we study the concepts of deficiency and ambiguity for a bijection on a finite Abelian group, in particular, for permutation polynomials over finite fields.Our focus is on all normalized permutation polynomials of degree less than or equal to 5. We obtain explicit numbers for deficiency and ambiguity of eleven classes of polynomials in Table A.0.1.We verified them by using SAGE.However, we could not find a formula for the last class of remaining two cases, except one observation on a relation between ambiguity and deficiency in a special case for one of the remaining unsolved classes.and mentor for my master's degree.Last but not the least, I would like to thank my family: my parents, (Altoumiyah Omar and Abduallah Musa Omar