English
Dr. Thomas Feulner
Kontaktdaten:
E-Mail: thomas.feulner@uni-bayreuth.de
Software:
My program CodeCan (online version) for the calculation of a canonical generator matrix of a linear code over a finite field and the rings Z4 and GF(2)[x]/(x2) written in C++. The source code is available under the terms of the GNU General Public License.
The algorithm is also implemented in Sage (since Version 6.1). See here for more details.
The Sage package codecan (applies to Sage 6.1) computes the canonical form of a linear code over any finite chain ring.
Computational results:
The following tables improve the upper bound on the minimum distance of a linear [n,k,d]q code.
Here is a list of pairwise CCZ-inequivalent APN functions calculated by this program.
Publications:
Computergestützte Berechnung eines eindeutigen Repräsentanten der semilinearen Isometrieklasse eines fehlerkorrigierenden, linearen Codes und Bestimmung der Automorphismengruppe (pdf), Diplomarbeit in Mathematik, Betreuer Prof. Dr. Kerber, Januar 2008
The Automorphism Groups of Linear Codes and Canonical Representatives of Their Semilinear Isometry Classes (link), Advances in Mathematics of Communications 3 (4), pp. 363-383, Nov 2009 (preprint)
Canonization of linear codes over Z4 (link), Advances in Mathematics of Communications 5 (2), pp. 245-266, May 2011
Classification and nonexistence results for linear codes with prescribed minimum distances (link), Designs, Codes and Cryptography, (preprint)
The automorphism group of a self-dual binary [72,36,16] code does not contain Z7, Z3xZ3 or D10 (link), IEEE Transactions on Information Theory (preprint) with Gabriele Nebe
Towards the Classification of Self-dual Bent Functions in Eight Variables (link), Designs, Codes and Cryptography, with Lin Sok, Patrick Solé and Alfred Wassermann
On canonical forms of ring-linear codes (link), Pre-proceedings of WCC2013, pp. 386-397, April 2013
Canonical Forms and Automorphisms in the Projective Space submitted to the Journal of Symbolic Computation (preprint)
PhD thesis:
Eine kanonische Form zur Darstellung äquivalenter Codes
- Computergestützte Berechnung und ihre Anwendung in der Codierungstheorie, Kryptographie und Geometrie -
Universität Bayreuth, Dissertation, 2013. - IX, 176 S. (link)
Talks:
The Automorphism Groups of Linear Codes and Canonical Representatives of Their Semilinear Isometry Classes (Kolkom 2009)
Canonization of linear codes over Z4 (Alcoma 2010)
Canonization of linear codes (S3CM 2010)
Isometry and Automorphisms of Constant Dimension Codes (Fq10)
Classification of Linear Codes with Prescribed Minimum Distance and New Upper Bounds (3ICMCTA)