Coding Theory; Network Coding; Constant Dimension Codes; Finite Grassmann Variety
Manganiello Felice, Trautmann Anna-Lena (2014), Spread decoding in extension fields, in Finite Fields and Their Applications
, 25(0), 94-105.
Rosenthal Joachim, Trautmann Anna-Lena (2013), A complete characterization of irreducible cyclic orbit codes and their Plucker embedding, in Des. Codes Cryptogr.
, 66(1-3), 275-289.
Rosenthal J., Trautmann A.-L. (2013), A Complete Characterization of Irreducible Cyclic Orbit Codes and their Plücker Embedding, in Des. Codes Cryptogr.
, 66(1--3), 275-289.
Trautmann A.-L., Manganiello F., Braun M., Rosenthal J. (2013), Cyclic Orbit Codes, in IEEE Transactions of Information Theory
, 59(11), 7386-7404.
Rosenthal J., Trautmann A.-L. (2013), Decoding of Subspace codes, a Problem of Schubert calculus over Finite Fields, in Hueper K. (ed.), CreateSpace, Seattle, Washington, 353-366.
Rosenthal J., Trautmann A.-L. (2013), Decoding of Subspace codes, a Problem of Schubert calculus over Finite Fields, in Hüper K. (ed.), CreateSpace, Part of Amazon group , 353-366.
Trautmann A.-L., Silberstein N., Rosenthal J. (2013), List Decoding of Lifted Gabidulin Codes via the Plücker Embedding, in Proceedings of the Seventh International Workshop on Coding and Cryptography (WCC)
, Bergen, NorwayWCC 2013, University of Bergen, Norway.
Silberstein N., Trautmann A.-L. (2013), New lower bounds for constant dimension codes, in IEEE International Symposium on Information Theory
, IEEE, New Jersey, USA.
Gorla Elisa, Manganiello Felice, Rosenthal Joachim (2012), An algebraic approach for decoding spread codes, in Adv. Math. Commun.
, 6(4), 443-466.
Tomas Virtudes, Rosenthal Joachim, Smarandache Roxana (2012), Decoding of convolutional codes over the erasure channel, in IEEE Trans. Inform. Theory
, 58(1), 90-108.
Fontein F., Marshall K., Rosenthal J., Schipani D., Trautmann A.-L. (2012), On Burst Error Correction and Storage Security of Noisy Data, in Proceedings of the 20th International Symposium MTNS
, MTNS, University of Melbourne.
Manganiello F., Trautmann A., Rosenthal J. (2012), On conjugacy classes of subgroups of the general linear group and cyclic orbit codes, in IEEE International Symposium on Information Theory ISIT 2011
, St. Petersburg, RussiaIEEE, New Jersey, USA.
Trautmann A.-L. (2012), Plücker Embedding of Cyclic Orbit Codes, in Proceedings of the 20th International Symposium MTNS
, MTNS, University of Melbourne.
Elia Michele, Rosenthal Joachim, Schipani Davide (2012), Polynomial evaluation over finite fields: new algorithms and complexity bounds, in Appl. Algebra Engrg. Comm. Comput.
, 23(3-4), 129-141.
Coding theory has emerged out of the need for bettercommunication and has rapidly developed as a mathematical theoryin strong relationship with algebra, combinatorics and algebraicgeometry. Nowadays error-correcting-codes are used in everydaypractical applications such as digital-storage media, wire-lineand wireless networks, and satellite and deep-space communicationsystems. Example of simple block codes are the internationalstandard book numbers (ISBN), the ASCII code and various encodingschemes used to identify bank accounts.Network coding theory is concerned with the encoding andtransmission of information where there may be many informationsources and possibly many receivers. R.~K\"otter andF.~Kschischang identified a fundamental mathematicalquestion which lies at the heart of network coding. Thisformulation seeks the construction of good subsets of thefinite Grassmann variety and it is the intended plan of theproposed research to use algebraic techniques to come up with newnetwork codes which have better performance.