Walsh spectra of all known APN functions over GF(2^8)

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The tables below contain the Walsh spectra for all quadratic APN functions of dimension 8 as given in the appendix of "A Matrix Approach for Constructing Quadratic APN Functions". All 8180 functions listed in the appendix have one of the following three Walsh spectra:

  • (same as the Gold functions)
  • (type 1)
  • (type 2)

There are 12 functions with a Walsh spectrum of type 2 (given in the table below), 487 functions with a Walsh spectrum of type 1, and 7681 functions with a Gold-like Walsh spectrum (not listed below due to space limitations). Magma code listing all functions with a Gold-like Walsh spectrum, a Walsh spectrum of type 1 and a Walsh spectrum of type 2 are available.


Functions with Walsh spectrum of type 2