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
AN - SCOPUS:84992735580
VL - 27
SP - 179
EP - 183
JO - Experimental Mathematics
JF - Experimental Mathematics
SN - 1058-6458
IS - 2
ER -