Abstract
A function f : GF(2r) → GF(2r) is called crooked if the sets {f(x) + f(x + a)|x ∈ GF(2r)} is an affine hyperplane for any nonzero a ∈ GF(2r). We prove that a crooked binomial function f(x) = x d + ux e defined on GF(2r) satisfies that both exponents d, e have 2-weights at most 2.
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Communicated by A. Pott.
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Bierbrauer, J., Kyureghyan, G.M. Crooked binomials. Des. Codes Cryptogr. 46, 269–301 (2008). https://doi.org/10.1007/s10623-007-9157-3
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DOI: https://doi.org/10.1007/s10623-007-9157-3
Keywords
- Crooked functions
- APN functions
- Codes
- Cyclotomic cosets
- Preparata codes
AMS Classifications
- 11T06
- 11T71