Abstract
The nonlinearity of a vectorial function over a finite field is defined in the paper as the Hamming distance from the function to the set of affine mappings in the space of values of all vectorial functions. For an arbitrary field of q elements we derive lower bounds for the nonlinearity of PN and APN functions in n variables in the form
Originally published in Diskretnaya Matematika (2023) 35, №4, 18–45 (in Russian).
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Artikel in diesem Heft
- Frontmatter
- On cosets in the direct product of groups whose images by bijective mappings from factors to groups are cosets
- On the linear disjunctive decomposition of a p-logic function into a sum of functions
- Hadamard square of series connected linear codes
- New bounds for the nonlinearity of PN functions and APN functions over finite fields
- Describing the closed class of polynomial functions modulo a power of a prime number by a relation
Artikel in diesem Heft
- Frontmatter
- On cosets in the direct product of groups whose images by bijective mappings from factors to groups are cosets
- On the linear disjunctive decomposition of a p-logic function into a sum of functions
- Hadamard square of series connected linear codes
- New bounds for the nonlinearity of PN functions and APN functions over finite fields
- Describing the closed class of polynomial functions modulo a power of a prime number by a relation