Complete description of a class of MDS-matrices over finite field of characteristic 2

We give complete description of the set of $n\times n$ MDS-matrices, $n>3$, over $GF(2^t)$, $t > 1$, with elements from the set $\{e,\alpha,\alpha^2\}$, where $e$ is an identity element, $\alpha\ne0$, $e$. It is proved that there are no such matrices if $n\geqslant6$. For $n = 4, 5$ the necessary and sufficient conditions of existence of MDS-matrices consisting of elements $e,\alpha,\alpha^2$ are given.