## Linear inequalities for covering codes

Publication
, Journal Article

Calderbank, AR; Sloane, NJA

December 1, 1988

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

## Publication Date

December 1, 1988

## Volume

25 n 13

## Start / End Page

33

### Citation

APA

Chicago

ICMJE

MLA

NLM

Calderbank, A. R., and N. J. A. Sloane. “Linear inequalities for covering codes” 25 n 13 (December 1, 1988): 33.

Calderbank AR, Sloane NJA. Linear inequalities for covering codes. 1988 Dec 1;25 n 13:33.

Calderbank, A. R., and N. J. A. Sloane.

*Linear inequalities for covering codes*. Vol. 25 n 13, Dec. 1988, p. 33.Calderbank AR, Sloane NJA. Linear inequalities for covering codes. 1988 Dec 1;25 n 13:33.

## Publication Date

December 1, 1988

## Volume

25 n 13

## Start / End Page

33