Math @ Duke
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Publications [#236026] of Robert Calderbank
Papers Published
- 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 2024/04/24)
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.
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