Abstract :
Let kq(n) denote the minimal cardinality of a q-ary code C of length n and covering radius one. The numbers of elements of C that lie in a fixed k-dimensional subspace of {0,…,q−1}n satisfy a certain system of linear inequalities. In a recent paper, the author developed a method to deal with this system for values of k, which are unbounded with increasing n. The aim of the present paper is to generalize the method in the cases q=2 and 3, which provides new lower bounds for k2(n) and k3(n).
