@article{Calderbank1988InequalitiesFC,
title={Inequalities for covering codes},
author={A. Robert Calderbank and N. J. A. Sloane},
journal={IEEE Trans. Information Theory},
year={1988},
volume={34},
pages={1276-1280}
}

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. The "syndrome graphs" associated with a linear code C help to 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 and t[23,15] = 3, where t [ n , k ] is the smallest covering radius of any [ n , k] code.