Construction of Constant Dimension Subspace Codes by Modifying Linkage Construction

The main problem of constant-dimension subspace coding is to construct constant-dimension codes (CDCs) with the maximum possible cardinality. Lifting Ferrers diagram codes is an effective way to construct CDCs. In addition, the discovery of linkage construction allows to construct many CDCs, i.e., lower bounds. In this paper, we combine the two methods of construction and obtain some new lower bounds of CDCs for small parameters.

[1]  Sascha Kurz,et al.  Coset Construction for Subspace Codes , 2015, IEEE Transactions on Information Theory.

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

[3]  Philippe Delsarte,et al.  Bilinear Forms over a Finite Field, with Applications to Coding Theory , 1978, J. Comb. Theory A.

[4]  Alberto Ravagnani,et al.  Optimal Ferrers Diagram Rank-Metric Codes , 2014, IEEE Transactions on Information Theory.

[5]  Natalia Silberstein,et al.  Codes and designs related to lifted MRD codes , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[6]  Sascha Kurz,et al.  Asymptotic Bounds for the Sizes of Constant Dimension Codes and an Improved Lower Bound , 2017, ICMCTA.

[7]  Tuvi Etzion,et al.  Problems on q-Analogs in Coding Theory , 2013, ArXiv.

[8]  Ron M. Roth,et al.  Author's Reply to Comments on 'Maximum-rank array codes and their application to crisscross error correction' , 1991, IEEE Trans. Inf. Theory.

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

[10]  Natalia Silberstein,et al.  Subspace Codes Based on Graph Matchings, Ferrers Diagrams, and Pending Blocks , 2014, IEEE Transactions on Information Theory.

[11]  Heide Gluesing-Luerssen,et al.  Construction of subspace codes through linkage , 2015, Adv. Math. Commun..

[12]  Alfred Wassermann,et al.  Tables of subspace codes , 2016, ArXiv.