TY - JOUR
T1 - Non-existence of a ternary constant weight (16, 5, 15; 2048) diameter perfect code
AU - Krotov, Denis S.
AU - Östergård, Patric R J
AU - Pottonen, Olli
PY - 2016/5/1
Y1 - 2016/5/1
N2 - Ternary constant weight codes of length n = 2m, weight n – 1, cardinality 2n and distance 5 are known to exist for every m for which there exists an APN permutation of order 2m, that is, at least for all odd m ≥ 3 and for m = 6. We show the non-existence of such codes for m = 4 and prove that any codes with the parameters above are diameter perfect.
AB - Ternary constant weight codes of length n = 2m, weight n – 1, cardinality 2n and distance 5 are known to exist for every m for which there exists an APN permutation of order 2m, that is, at least for all odd m ≥ 3 and for m = 6. We show the non-existence of such codes for m = 4 and prove that any codes with the parameters above are diameter perfect.
KW - Constant weight code
KW - Diameter perfect code
UR - http://www.scopus.com/inward/record.url?scp=84964786809&partnerID=8YFLogxK
U2 - 10.3934/amc.2016013
DO - 10.3934/amc.2016013
M3 - Article
AN - SCOPUS:84964786809
VL - 10
SP - 393
EP - 399
JO - Advances in Mathematics of Communications
JF - Advances in Mathematics of Communications
SN - 1930-5346
IS - 2
ER -