Linear inequalities for covering codes

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 Scholars

Author Robert Calderbank Computer Science