A note on the linkage construction for constant dimension codes

Constant dimension codes are used for error control in random linear network coding, so that constructions for these codes with large cardinality have achieved wide attention in the last decade. Here, we improve the so-called linkage construction and obtain several parametric series of improvements for code the sizes.

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

[2]  Daniel Heinlein,et al.  New LMRD Code Bounds for Constant Dimension Codes and Improved Constructions , 2018, IEEE Transactions on Information Theory.

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

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

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

[6]  Alfred Wassermann,et al.  A subspace code of size 333 in the setting of a binary q-analog of the Fano plane , 2017, Adv. Math. Commun..

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

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

[9]  Giuseppe Marino,et al.  Subspace code constructions , 2019, ArXiv.

[10]  Daniel Heinlein.  Generalized Linkage Construction for Constant-Dimension Codes , 2021, IEEE Transactions on Information Theory.

[11]  Sascha Kurz,et al.  Optimal binary subspace codes of length 6, constant dimension 3 and minimum distance 4 , 2014 .

[12]  Thomas Honold,et al.  On putative q-analogues of the Fano plane and related combinatorial structures , 2015, 1504.06688.

[13]  Sascha Kurz.  Subspaces intersecting in at most a point , 2020, Des. Codes Cryptogr..

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

[15]  Hao Chen,et al.  New Constant-Dimension Subspace Codes from Maximum Rank Distance Codes , 2018, IEEE Transactions on Information Theory.

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

[17]  Albrecht Beutelspacher,et al.  Partial spreads in finite projective spaces and partial designs , 1975 .

[18]  Antonio Cossidente,et al.  Combining subspace codes , 2019, ArXiv.

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