# Linear inequalities for covering codes

Published

Journal Article

Summary form only given, as follows. 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.

### Duke Authors

### Cited Authors

- Calderbank, AR; Sloane, NJA

### Published Date

- December 1, 1988

### Volume / Issue

- 25 n 13 /

### Start / End Page

- 33 -

### Citation Source

- Scopus