TY - JOUR
T1 - On the existence of extended perfect binary codes with trivial symmetry group
AU - Heden, Olof
AU - Pasticci, Fabio
AU - Westerbäck, Thomas
PY - 2009/8
Y1 - 2009/8
N2 - The set of permutations of the coordinate set that maps a perfect code C into itself is called the symmetry group of C and is denoted by Sym(C). It is proved that for all integers n = 2m - 1, where m = 4, 5, 6, . . . , and for any integer r, where n - log(n + 1) + 3≤ r≤ n - 1, there are perfect codes of length n and rank r with a trivial symmetry group, i.e. Sym(C) = {id}. The result is shown to be true, more generally, for the extended perfect codes of length n + 1.
AB - The set of permutations of the coordinate set that maps a perfect code C into itself is called the symmetry group of C and is denoted by Sym(C). It is proved that for all integers n = 2m - 1, where m = 4, 5, 6, . . . , and for any integer r, where n - log(n + 1) + 3≤ r≤ n - 1, there are perfect codes of length n and rank r with a trivial symmetry group, i.e. Sym(C) = {id}. The result is shown to be true, more generally, for the extended perfect codes of length n + 1.
KW - Perfect codes
KW - Symmetry group
UR - http://www.scopus.com/inward/record.url?scp=69249097938&partnerID=8YFLogxK
U2 - 10.3934/amc.2009.3.295
DO - 10.3934/amc.2009.3.295
M3 - Article
AN - SCOPUS:69249097938
VL - 3
SP - 295
EP - 309
JO - Advances in Mathematics of Communications
JF - Advances in Mathematics of Communications
SN - 1930-5346
IS - 3
ER -