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 (January, 1988), pp. 1276-1280, Institute of Electrical and Electronics Engineers (IEEE) [doi]
   (last updated on 2026/01/18)

   Abstract:
   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. 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. © 1988 IEEE.