Construction of subspace codes through linkage

Gluesing-Luerssen, Heide; Troha, Carolyn

doi:10.3934/amc.2016023

Cited by 66 publications

(37 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In this paper firstly we give a parallel linkage construction based on the linkage construction proposed by Gluesing-Luerssen and Troha in [10]. The basic idea is to use parallel versions of linkage and to give a suitable sufficient condition such that the subspace distance can be preserved for picking up subsets in these parallel blocks.…”

Section: Introductionmentioning

confidence: 99%

New Constructions of Subspace Codes Using Subsets of MRD Codes in Several Blocks

Chen

Weng

et al. 2020

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

A basic problem for the constant dimension subspace coding is to determine the maximal possible size A q (n, d, k) of a set of k-dimensional subspaces in F n q such that the subspace distance satisfies d(U, V ) = 2k − 2 dim(U ∩ V ) ≥ d for any two different subspaces U and V in this set. We present two new constructions of constant dimension subspace codes using subsets of maximal rank-distance (MRD) codes in several blocks. This method is firstly applied to the linkage construction and secondly to arbitrary number of blocks of lifting MRD codes. In these two constructions subsets of MRD codes with bounded ranks play an essential role. The Delsarte theorem of the rank distribution of MRD codes is an important ingredient to count codewords in our constructed constant dimension subspace codes. We give many new lower bounds for A q (n, d, k). More than 110 new constant dimension subspace codes better than previously best known codes are constructed.

show abstract

Section: Introductionmentioning

confidence: 99%

New Constructions of Subspace Codes Using Subsets of MRD Codes in Several Blocks

Chen

Weng

et al. 2020

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

“…| 0 | w) both having rank distance at least d for d ≥ 2. Hence, this corollary constructs codes of the same size as Theorem 4.6 in [22] but these codes are not necessarily equal.…”

Section: Instead Ofmentioning

confidence: 99%

“…However, it can be used to prove: Corollary 6 (cf. [22,Theorem 4.6]). Let C R be an (k × v 1 + v 2 , d) q linear MRD code, where k ≤ v i , for i = 1, 2 and let C i be an (v i−2 , N i , 2d; k) q constant dimension codes for i = 3, 4.…”

Section: Instead Ofmentioning

confidence: 99%

Asymptotic Bounds for the Sizes of Constant Dimension Codes and an Improved Lower Bound

Heinlein

Kurz

2017

Coding Theory and Applications

View full text Add to dashboard Cite

We study asymptotic lower and upper bounds for the sizes of constant dimension codes with respect to the subspace or injection distance, which is used in random linear network coding. In this context we review known upper bounds and show relations between them. A slightly improved version of the so-called linkage construction is presented which is e.g. used to construct constant dimension codes with subspace distance d = 4, dimension k = 3 of the codewords for all field sizes q, and sufficiently large dimensions v of the ambient space, that exceed the MRD bound, for codes containing a lifted MRD code, by Etzion and Silberstein.

show abstract

“…In [42] the authors also study which of the known constructions for constant-dimension codes yield the currently best known lower bounds for A q (n, k, t; 1) in the most most number of cases. The two most successful approaches are the echelon-Ferrers Construction (including their different variants) and the so-called linkage construction [38]. We remark that improvements of the original linkage construction were obtained in [43,63].…”

Section: Constructions For Subspace Packingsmentioning

confidence: 99%

Subspace packings: constructions and bounds

Etzion

Kurz

Otal

et al. 2020

Des. Codes Cryptogr.

View full text Add to dashboard Cite

The Grassmannian G q (n, k) is the set of all k-dimensional subspaces of the vector space F n q . Kötter and Kschischang showed that codes in Grassmannian space can be used for error-correction in random network coding. On the other hand, these codes are qanalogs of codes in the Johnson scheme, i.e. constant dimension codes. These codes of the Grassmannian G q (n, k) also form a family of q-analogs of block designs and they are called subspace designs.In this paper, we examine one of the last families of q-analogs of block designs which was not considered before. This family called subspace packings is the q-analog of packings, and was considered recently for network coding solution for a family of multicast networks called the generalized combination networks. A subspace packing t-(n, k, λ) q is a set S of k-subspaces from G q (n, k) such that each t-subspace of G q (n, t) is contained in at most λ elements of S. The goal of this work is to consider the largest size of such subspace packings. We derive a sequence of lower and upper bounds on the maximum size of such packings, analyse these bounds, and identify the important problems for further research in this area.

show abstract

Construction of subspace codes through linkage

Cited by 66 publications

References 32 publications

New Constructions of Subspace Codes Using Subsets of MRD Codes in Several Blocks

New Constructions of Subspace Codes Using Subsets of MRD Codes in Several Blocks

Asymptotic Bounds for the Sizes of Constant Dimension Codes and an Improved Lower Bound

Subspace packings: constructions and bounds

Contact Info

Product

Resources

About