INEQUALITIES FOR COVERING CODES

Any code C with covering radius R must satisfy a set of linear inequalities that involve the Lloyd polynomial LR(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). As illustrations it is shown that t[17,10]=3 nd t[23,15]=3 where t[n,k] is the smallest covering radius of any [n,k] code.