# Program that calculates the canonical generator matrix and the automorphism group of a linear code over a chain ring with 4 elements

This program computes a unique generator matrix under all generator matrices of linearly isometric, linear codes over the rings Z_{4} and F_{2}[X]/(X^{2}).

We applied the program for a full classification of the linear codes with small parameters.

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

Please, enter some generator matrix in the following form.

**Example:**The Kerdock code K(3)

*n*=8,

*k*=4

1 0 0 0 3 1 2 1 0 1 0 0 2 1 1 3 0 0 1 0 1 1 3 2 0 0 0 1 3 2 3 3

The elements of F_{2}[X]/(X^{2}) are decoded by 0=0, 1=1, X=2, 1+X=3

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.