On quasi-cyclic subspace codes

Construction of subspace codes with good parameters is one of the most important problems in random network coding. In this paper we present first a generalization of the concept of cyclic subspaces codes and further we show that the usual methods for constructing cyclic subspace codes over finite fields works for m-quasi cyclic codes, namely the subspaces polynomials and Frobenius mappings.

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

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

[3]  Ronald L. Graham,et al.  Concrete mathematics - a foundation for computer science , 1991 .

[4]  H. Niederreiter,et al.  Introduction to finite fields and their applications: Factorization of Polynomials , 1994 .

[5]  Ismael Gutierrez,et al.  Some constructions of cyclic and quasi-cyclic subspaces codes , 2015 .

[6]  Heide Gluesing-Luerssen,et al.  Cyclic orbit codes and stabilizer subfields , 2015, Adv. Math. Commun..

[7]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[8]  O. Ore On a special class of polynomials , 1933 .

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

[10]  Jörg Widmer,et al.  Network coding: an instant primer , 2006, CCRV.

[11]  Eli Ben-Sasson,et al.  Subspace Polynomials and Cyclic Subspace Codes , 2014, IEEE Transactions on Information Theory.

[12]  Jaikumar Radhakrishnan,et al.  Subspace Polynomials and List Decoding of Reed-Solomon Codes , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

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

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