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Inequalities for covering codes

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2 Author(s)
Calderbank, A.R. ; AT&T Bell Lab., Murray Hill, NJ, USA ; Sloane, N.

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. 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). Illustrations show 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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Information Theory, IEEE Transactions on  (Volume:34 ,  Issue: 5 )