# Program that calculates the canonical generator matrix of a linear code and the automorphism group under the action of the linear or semilinear isometry group (article)

List of pairwise CCZ-inequivalent APN Functions

This program computes a unique generator matrix under all generator matrices of (semi-)linearly isometric, linear codes over arbitrary fields, the field elements are numbered by 0, ..., q-1 with q = p^{r}, p prime. The numbering N is based on a root ξ of the Conway Polynomial of degree r:

_{i = 0,..., r-1}μ

_{i}ξ

^{i}⇒ N(μ) = ∑

_{i = 0,..., r-1}μ

_{i}p

^{i}

You can use any generator matrix over the fields GF(q) with q = 2, 3, 4, 5, 7, 8, 9, 16, 32.

The program returns the elements of the acting group by tupels (A, φ, α, π) with an invertible k × k matrix A, a vector of nonzero column multiplications φ, a field automorphism α and a permutation of columns π .

Please, enter some generator matrix in the following form.

**Example:**The quadratic residue code C(11,6) over GF(3).

*n*=11,

*k*=6,

*q*=3:

2 2 1 2 0 1 0 0 0 0 0 0 2 2 1 2 0 1 0 0 0 0 0 0 2 2 1 2 0 1 0 0 0 0 0 0 2 2 1 2 0 1 0 0 0 0 0 0 2 2 1 2 0 1 0 0 0 0 0 0 2 2 1 2 0 1

You can also use this code for the field GF(9), where you can see the difference between semilinear and linear isometry.

The algorithm is implemented in the programming language C++, but we use the computer algebra system Magma to compute the group of known automorphism in the backtrack search.

The execution time of this online version is limited to 2 minutes.

Last Modified: 2012-07-06.