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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.

Authors :
Gupta, Prachi
Mishra, P. R.
Gaur, Atul
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]

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