A geometric construction of a [10,5,90]_9-linear code admitting the Mathieu group M_{11}

In 1978 R. Hill introduced a construction of linear codes arising from caps called cap-codes. Cap-codes corresponding to complete caps are particularly interesting, not only for having minimum distance greater than 3, but also because their dual codes have covering radius $2$, that is, all vectors in the Hamming space $V(n,q)$ have distance at most $2$ from some word of the code. Codes with small covering radius are useful for data compression since the value of covering radius gives a measure of maximum distorsion. In this paper we give a geometric construction of a $[110,5,90]_{9}$-linear code admitting the Mathieu group $M_{11}$ as a subgroup of its automorphism group.