Scholars@Duke

Inequalities for Covering Codes

Publication ,  Journal Article
Calderbank, AR; Sloane, NJA
Published in: IEEE Transactions on Information Theory
January 1, 1988
Published version (DOI)

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. © 1988 IEEE.

Duke Scholars

Robert Calderbank
Author Robert Calderbank Computer Science

Published In

IEEE Transactions on Information Theory

DOI

10.1109/18.21257

EISSN

1557-9654

ISSN

0018-9448

Publication Date

January 1, 1988

Volume

34

Issue

5

Start / End Page

1276 / 1280

Related Subject Headings

  • Networking & Telecommunications
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing
 

Citation

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Calderbank, A. R., & Sloane, N. J. A. (1988). Inequalities for Covering Codes. IEEE Transactions on Information Theory, 34(5), 1276–1280. https://doi.org/10.1109/18.21257
Calderbank, A. R., and N. J. A. Sloane. “Inequalities for Covering Codes.” IEEE Transactions on Information Theory 34, no. 5 (January 1, 1988): 1276–80. https://doi.org/10.1109/18.21257.
Calderbank AR, Sloane NJA. Inequalities for Covering Codes. IEEE Transactions on Information Theory. 1988 Jan 1;34(5):1276–80.
Calderbank, A. R., and N. J. A. Sloane. “Inequalities for Covering Codes.” IEEE Transactions on Information Theory, vol. 34, no. 5, Jan. 1988, pp. 1276–80. Scopus, doi:10.1109/18.21257.
Calderbank AR, Sloane NJA. Inequalities for Covering Codes. IEEE Transactions on Information Theory. 1988 Jan 1;34(5):1276–1280.

Published In

IEEE Transactions on Information Theory

DOI

10.1109/18.21257

EISSN

1557-9654

ISSN

0018-9448

Publication Date

January 1, 1988

Volume

34

Issue

5

Start / End Page

1276 / 1280

Related Subject Headings

  • Networking & Telecommunications
  • 1005 Communications Technologies
  • 0906 Electrical and Electronic Engineering
  • 0801 Artificial Intelligence and Image Processing