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 Z4 and F2[X]/(X2).
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=41 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 F2[X]/(X2) 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.