Publications [#236026] of Robert Calderbank

Journal articles or Book chapters PUBLISHED
  1. Calderbank, AR; Sloane, NJA, Inequalities for covering codes, IEEE Transactions on Information Theory, vol. 34 no. 5 pt 2 (1988), pp. 1276-1280 [doi] .

    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.