# New Lower Bounds for Binary Constant-Dimension Subspace Codes

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**New Lower Bounds for Binary Constant-Dimension Subspace Codes.** / Braun, Michael; Östergård, Patric R J; Wassermann, Alfred.

Research output: Contribution to journal › Article › Scientific › peer-review

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*Experimental Mathematics*, vol. 27, no. 2, pp. 179-183. https://doi.org/10.1080/10586458.2016.1239145

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*Experimental Mathematics*,

*27*(2), 179-183. https://doi.org/10.1080/10586458.2016.1239145

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TY - JOUR

T1 - New Lower Bounds for Binary Constant-Dimension Subspace Codes

AU - Braun, Michael

AU - Östergård, Patric R J

AU - Wassermann, Alfred

PY - 2018

Y1 - 2018

N2 - Let (Formula presented.) denote the maximum cardinality of a set (Formula presented.) of k-dimensional subspaces of an n-dimensional vector space over the finite field of order q, (Formula presented.), such that any two different subspaces (Formula presented.) have a distance (Formula presented.) of at least d. Lower bounds on (Formula presented.) can be obtained by explicitly constructing corresponding sets (Formula presented.). When searching for such sets with a prescribed group of automorphisms, the search problem leads to instances of the maximum weight clique problem. The main focus is here on subgroups with small index in the normalizer of a Singer subgroup of (Formula presented.). With a stochastic maximum weight clique algorithm and a systematic consideration of groups of the above mentioned type, new lower bounds on (Formula presented.) and (Formula presented.) for 8 ⩽ n ⩽ 11 are obtained.

AB - Let (Formula presented.) denote the maximum cardinality of a set (Formula presented.) of k-dimensional subspaces of an n-dimensional vector space over the finite field of order q, (Formula presented.), such that any two different subspaces (Formula presented.) have a distance (Formula presented.) of at least d. Lower bounds on (Formula presented.) can be obtained by explicitly constructing corresponding sets (Formula presented.). When searching for such sets with a prescribed group of automorphisms, the search problem leads to instances of the maximum weight clique problem. The main focus is here on subgroups with small index in the normalizer of a Singer subgroup of (Formula presented.). With a stochastic maximum weight clique algorithm and a systematic consideration of groups of the above mentioned type, new lower bounds on (Formula presented.) and (Formula presented.) for 8 ⩽ n ⩽ 11 are obtained.

KW - constant-dimension codes

KW - integer linear programming

KW - packing

KW - random network coding

UR - http://www.scopus.com/inward/record.url?scp=84992735580&partnerID=8YFLogxK

U2 - 10.1080/10586458.2016.1239145

DO - 10.1080/10586458.2016.1239145

M3 - Article

VL - 27

SP - 179

EP - 183

JO - Experimental Mathematics

JF - Experimental Mathematics

SN - 1058-6458

IS - 2

ER -

ID: 9202555