Geodesic
Complete description of a class of MDS-matrices over finite field of characteristic~2
Matematičeskie voprosy kriptografii, Tome 8 (2017), pp. 5-28

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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. 
@article{MVK_2017_8_a0,
     author = {A. V. Anashkin},
     title = {Complete description of a class of {MDS-matrices} over finite field of characteristic~2},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {5--28},
     publisher = {mathdoc},
     volume = {8},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2017_8_a0/}
}
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A. V. Anashkin. Complete description of a class of MDS-matrices over finite field of characteristic~2. Matematičeskie voprosy kriptografii, Tome 8 (2017), pp. 5-28. http://geodesic.mathdoc.fr/item/MVK_2017_8_a0/