Isometry and automorphisms of constant dimension codes

We define linear and semilinear isometry for general subspace codes, used for random network coding. Furthermore, some results on isometry classes and automorphism groups of known constant dimension code constructions are derived.

[1]  Sascha Kurz,et al.  Construction of Large Constant Dimension Codes with a Prescribed Minimum Distance , 2008, MMICS.

[2]  J. Hirschfeld Finite projective spaces of three dimensions , 1986 .

[3]  Anna-Lena Horlemann-Trautmann,et al.  Spread decoding in extension fields , 2011, Finite Fields Their Appl..

[4]  Vitaly Skachek,et al.  Recursive Code Construction for Random Networks , 2008, IEEE Transactions on Information Theory.

[5]  Frank R. Kschischang,et al.  Coding for Errors and Erasures in Random Network Coding , 2008, IEEE Trans. Inf. Theory.

[6]  Frank R. Kschischang,et al.  On Metrics for Error Correction in Network Coding , 2008, IEEE Transactions on Information Theory.

[7]  Joachim Rosenthal,et al.  Cyclic Orbit Codes , 2011, IEEE Transactions on Information Theory.

[8]  Thierry P. Berger,et al.  Isometries for rank distance and permutation group of Gabidulin codes , 2003, IEEE Trans. Inf. Theory.

[9]  J. Thas,et al.  General Galois geometries , 1992 .

[10]  Joachim Rosenthal,et al.  An algebraic approach for decoding spread codes , 2012, Adv. Math. Commun..

[11]  Joachim Rosenthal,et al.  Orbit codes — A new concept in the area of network coding , 2010, 2010 IEEE Information Theory Workshop.

[12]  Frank R. Kschischang,et al.  Subspace Codes , 2009, IMACC.

[13]  Peter Wild,et al.  FINITE PROJECTIVE SPACES OF THREE DIMENSIONS (Oxford Mathematical Monographs) , 1987 .

[14]  Alexander Vardy,et al.  Error-correcting codes in projective space , 2008, 2008 IEEE International Symposium on Information Theory.

[15]  Natalia Silberstein,et al.  Error-Correcting Codes in Projective Spaces Via Rank-Metric Codes and Ferrers Diagrams , 2008, IEEE Transactions on Information Theory.

[16]  R. Baer,et al.  Linear algebra and projective geometry , 1952 .

[17]  Frank R. Kschischang,et al.  A Rank-Metric Approach to Error Control in Random Network Coding , 2007, IEEE Transactions on Information Theory.

[18]  Frank R. Kschischang,et al.  Coding for Errors and Erasures in Random Network Coding , 2007, IEEE Transactions on Information Theory.

[19]  Joachim Rosenthal,et al.  Spread codes and spread decoding in network coding , 2008, 2008 IEEE International Symposium on Information Theory.

[20]  Rudolf Ahlswede,et al.  Network information flow , 2000, IEEE Trans. Inf. Theory.

[21]  Thomas Feulner Canonical Forms and Automorphisms in the Projective Space , 2013, ArXiv.