Inequalities for covering codes

@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. 

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Short codes with a given covering radius

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