scholarly journals Classifying optimal binary subspace codes of length 8, constant dimension 4 and minimum distance 6

2018 ◽  
Vol 87 (2-3) ◽  
pp. 375-391 ◽  
Author(s):  
Daniel Heinlein ◽  
Thomas Honold ◽  
Michael Kiermaier ◽  
Sascha Kurz ◽  
Alfred Wassermann
Keyword(s):  
Minimum Distance ◽  
Subspace Codes ◽  
Constant Dimension

New constant dimension subspace codes from generalized inserting construction

2020 ◽  
pp. 1-1
Author(s):  
Yongfeng Niu ◽  
Qin Yue ◽  
Daitao Huang
Keyword(s):  
Subspace Codes ◽  
Constant Dimension

Improvement to the sunflower bound for a class of equidistant constant dimension subspace codes

2021 ◽  
Vol 112 (1) ◽  
Author(s):  
D. Bartoli ◽  
A.-E. Riet ◽  
L. Storme ◽  
P. Vandendriessche
Keyword(s):  
Subspace Codes ◽  
Constant Dimension

scholarly journals On sets of subspaces with two intersection dimensions and a geometrical junta bound

2021 ◽  
Author(s):  
Giovanni Longobardi ◽  
Leo Storme ◽  
Rocco Trombetti
Keyword(s):  
Vector Space ◽  
Upper Bound ◽  
Subspace Codes ◽  
Constant Dimension ◽  
Subspace Distance

AbstractIn this article, constant dimension subspace codes whose codewords have subspace distance in a prescribed set of integers, are considered. The easiest example of such an object is a junta (Combin Probab Comput 18(1–2):107–122, 2009); i.e. a subspace code in which all codewords go through a common subspace. We focus on the case when only two intersection values for the codewords, are assigned. In such a case we determine an upper bound for the dimension of the vector space spanned by the elements of a non-junta code. In addition, if the two intersection values are consecutive, we prove that such a bound is tight, and classify the examples attaining the largest possible dimension as one of four infinite families.

scholarly journals Johnson Type Bounds for Mixed Dimension Subspace Codes

10.37236/8188 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Thomas Honold ◽  
Michael Kiermaier ◽  
Sascha Kurz
Keyword(s):  
Network Coding ◽  
Upper Bounds ◽  
Linear Network ◽  
Subspace Codes ◽  
Linear Network Coding ◽  
Constant Dimension ◽  
Random Linear Network Coding ◽  
Johnson Bound ◽  
Constant Dimension Codes ◽  
Mixed Dimension

Subspace codes, i.e., sets of subspaces of $\mathbb{F}_q^v$, are applied in random linear network coding. Here we give improved upper bounds for their cardinalities based on the Johnson bound for constant dimension codes.

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