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On Inverses of Permutation Polynomials of Small Degree Over Finite Fields.
- Source :
-
IEEE Transactions on Information Theory . Feb2020, Vol. 66 Issue 2, p914-922. 9p. - Publication Year :
- 2020
-
Abstract
- Permutation polynomials (PPs) and their inverses have applications in cryptography, coding theory and combinatorial design theory. In this paper, we make a brief summary of the inverses of PPs of finite fields, and give the inverses of all PPs of degree ≤ 6 over finite fields $\mathbb {F}_{q}$ for all $q$ and the inverses of all PPs of degree 7 over $\mathbb {F}_{2^{n}}$. The explicit inverse of a class of fifth degree PPs is the main result, which is obtained by using Lucas’ theorem, some congruences of binomial coefficients, and a known formula for the inverses of PPs of finite fields. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 66
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 141381289
- Full Text :
- https://doi.org/10.1109/TIT.2019.2939113