Inequalities for covering codes

Any code C with covering radius R must satisfy a set of linear inequalities that involve the Lloyd polynomial L/sub 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.<
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