A note on maximum distance separable (optimal) codes (Corresp.)

Given a positive integer
k
and a prime power
q
with
q \leq k
, it is proved that the largest value of
n
for which there exists an
[n,k,n-k+l]
maximum distance separable (MDS) code over GF
(q)
is
k+1
. A simple proof for the largest value of
n
for which there exists an
[n,2,n-1]
MDS code over any finite field is also given.