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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

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Calderbank, A. R., & Sloane, N. J. A. (1988). Linear inequalities for covering codes, 25 n 13, 33.
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