Binary and ternary codes of covering radius one: some new lower bounds (Q1849922)

The aim of this paper is to generalize the method developed by the author in an earlier paper in the cases \(q=2\) and \(q=3\) which provide new lower obunds for \(k_2(n)\) and \(k_3(n)\), where \(k_q(n)\) denotes the minimal cardinality of a \(q\)-ary code \(C\) of length \(n\) and covering radius one. Section 3 of the paper is devoted to the binary case with improvements on already known lower bounds for \(k_2(n)\) in the cases \(n= 19,21,25,27\) and \(33\). Section 4 contains the ternary case (known as the football pool problem) with new lower bounds for \(k_3(8)\) and \(k_3(10)\).