TY - JOUR
T1 - Constructing error-correcting binary codes using transitive permutation groups
AU - Laaksonen, Antti
AU - Östergård, Patric R.J.
PY - 2017
Y1 - 2017
N2 - Transitive permutation groups are recurrent in the study of automorphism groups of combinatorial objects. For binary error-correcting codes, groups are here considered that act transitively on the pairs of coordinates and coordinate values. By considering such groups in an exhaustive manner and carrying out computer searches, the following new bounds are obtained on A2(n,d), the maximum size of a binary code of length n and minimum distance d: A2(17,3)≥5632, A2(20,3)≥40960, A2(21,3)≥81920, A2(22,3)≥163840, A2(23,3)≥327680, A2(23,9)≥136, and A2(24,5)≥17920.
AB - Transitive permutation groups are recurrent in the study of automorphism groups of combinatorial objects. For binary error-correcting codes, groups are here considered that act transitively on the pairs of coordinates and coordinate values. By considering such groups in an exhaustive manner and carrying out computer searches, the following new bounds are obtained on A2(n,d), the maximum size of a binary code of length n and minimum distance d: A2(17,3)≥5632, A2(20,3)≥40960, A2(21,3)≥81920, A2(22,3)≥163840, A2(23,3)≥327680, A2(23,9)≥136, and A2(24,5)≥17920.
KW - Binary codes
KW - Cliques
KW - Error-correcting codes
KW - Transitive groups
UR - http://www.scopus.com/inward/record.url?scp=85030458329&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2017.08.022
DO - 10.1016/j.dam.2017.08.022
M3 - Article
AN - SCOPUS:85030458329
SN - 0166-218X
VL - 233
SP - 65
EP - 70
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -