By using a method of construction of block-primitive and point-transitive 1-designs, in this paper we determine all block-primitive and point-transitive 1-((v, k, lambda))-designs from the maximal subgroups and the conjugacy classes of elements of the small Mathieu group ({rm M}_{11}). We examine the properties of the 1-((v, k, lambda))-designs and construct the codes defined by the binary row span of their incidence matrices. Furthermore, we present a number of interesting (Delta)-divisible binary codes invariant under ({rm M}_{11})
