Deficiency and Ambiguity of Low Degree Permutation Polynomials
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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 ≤ 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 can not do much for the remaining two cases, except one observation on a relation between ambiguity and deficiency in a special case for one of the remaining unsolved classes.
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Copyright © 2016 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
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