Inequalities for covering codes

Any code C with covering radius R must satisfy a set of linear inequalities that involve the Lloyd polynomial L _R(x); these generalize the sphere bound. Syndrome graphs associated with a linear code C are introduced to help keep track of low-weight vectors in the same coset of C (if there are too many such vectors C cannot exist). Illustrations show that t[17, 10]=3 and t[23, 15]=3 where t[n, k] is the smallest covering radius of any [n, k] code