Back to Search
Start Over
Bounds on the maximum nonlinearity of permutations on the rings Zp and Z2p.
Bounds on the maximum nonlinearity of permutations on the rings Zp and Z2p.
- Source :
- Applicable Algebra in Engineering, Communication & Computing; Nov2024, Vol. 35 Issue 6, p859-874, 16p
- Publication Year :
- 2024
-
Abstract
- In 2016, Y. Kumar et al. in the paper 'Affine equivalence and non-linearity of permutations over Z n ' conjectured that: For n ≥ 3 , the nonlinearity of any permutation on Z n , the ring of integers modulon, cannot exceed n - 2 . For an odd prime p, we settle the above conjecture when n = 2 p and for p ≡ 3 (mod 4) we prove the above conjecture with an improved upper bound. Further, we derive a lower bound on max N L n when n is an odd prime or twice of an odd prime where max N L n denotes the maximum possible nonlinearity of any permutation on Z n . [ABSTRACT FROM AUTHOR]
- Subjects :
- RINGS of integers
FINITE fields
LOGICAL prediction
UNIFORMITY
PERMUTATIONS
Subjects
Details
- Language :
- English
- ISSN :
- 09381279
- Volume :
- 35
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Applicable Algebra in Engineering, Communication & Computing
- Publication Type :
- Academic Journal
- Accession number :
- 180269447
- Full Text :
- https://doi.org/10.1007/s00200-022-00594-z