Complete
n-tracks in
CDTF-2&_mathId=mml1&_user=10&_cdi=6798&_rdoc=24&_acct=C000050221&_version=1&_userid=10&md5=9680ba189690dd4e49773f7ee8e667da"" title=""Click to view the MathML source"">PG(N,q) and non-extendable Near MDS codes of dimension
N+1 over
Fq are known to be equivalent objects. The best known lower bound for the maximum number of points of an
n-track is attained by elliptic
n-tracks, that is,
n-tracks consisting of the
Fq-rational points of an elliptic curve. This has given a motivation for the study of complete elliptic
n-tracks. From previous work, an elliptic
n-track in
PG(2,q) is complete provided that either the
j-invariant
![]()
of the underlying elliptic curve
![]()
is different from zero, or
![]()
and the number
Nq of
Fq-rational points of
![]()
is even. In this paper it is shown that the latter result extends to odd
Nq if and only if either
q is a square or
![]()
,
p being the characteristic of
Fq. Some completeness results for elliptic
n-tracks in dimensions 3 and 5 are also obtained.