# Difference between revisions of "Tables"

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* [[CCZ-invariants for all known APN functions in dimension 7]] | * [[CCZ-invariants for all known APN functions in dimension 7]] | ||

* [[CCZ-invariants for all known APN functions in dimension 8]] | * [[CCZ-invariants for all known APN functions in dimension 8]] | ||

+ | * [[Sigma multiplicities for APN functions in dimensions up to 10]] | ||

=== Other instances === | === Other instances === | ||

* [[Known switching classes of APN functions over GF(2^n) for n = 5,6,7,8]] | * [[Known switching classes of APN functions over GF(2^n) for n = 5,6,7,8]] | ||

+ | * [[APN functions obtained via polynomial expansion in small dimensions]] | ||

* [[Classification of Quadratic APN Trinomials, Quadrinomials, Pentanomials, Hexanomials (CCZ-inequivalent with infinite monomial families) in Small Dimensions with all Coefficients equal to 1]] | * [[Classification of Quadratic APN Trinomials, Quadrinomials, Pentanomials, Hexanomials (CCZ-inequivalent with infinite monomial families) in Small Dimensions with all Coefficients equal to 1]] | ||

* [[APN polynomials over GF(2^n) CCZ-inequivalent to quadratic functions and monomials]] | * [[APN polynomials over GF(2^n) CCZ-inequivalent to quadratic functions and monomials]] |

## Latest revision as of 18:15, 3 January 2023

# Known instances of APN functions over

## Known families of APN functions

- Known infinite families of APN power functions over GF(2^n)
- Known infinite families of quadratic APN polynomials over GF(2^n)

## On known instances in small dimensions

### Power functions

- APN power functions over GF(2^n) with n less than or equal to 13
- Inverses of known APN power permutations over GF(2^n) with n less than or equal to 129

### Quadratic functions

### Equivalences, inequivalences and invariants

- CCZ-inequivalent representatives from the known APN families for dimensions up to 11
- Walsh spectra of all known APN functions over GF(2^8)
- CCZ-equivalence of Families of APN Polynomials over GF(2^n) from the table (for n between 6 and 11)
- CCZ-invariants for all known APN functions in dimension 7
- CCZ-invariants for all known APN functions in dimension 8
- Sigma multiplicities for APN functions in dimensions up to 10

### Other instances

- Known switching classes of APN functions over GF(2^n) for n = 5,6,7,8
- APN functions obtained via polynomial expansion in small dimensions
- Classification of Quadratic APN Trinomials, Quadrinomials, Pentanomials, Hexanomials (CCZ-inequivalent with infinite monomial families) in Small Dimensions with all Coefficients equal to 1
- APN polynomials over GF(2^n) CCZ-inequivalent to quadratic functions and monomials
- Lower bounds on APN-distance for all known APN functions

## Misceallaneous results

- Some APN functions CCZ-equivalent to Gold functions and EA-inequivalent to power functions over GF(2^n)
- Some APN functions CCZ-equivalent to x^3 + tr_n(x^9) and CCZ-inequivalent to the Gold functions over GF(2^n)