Abstract
We further develop techniques for showing the non-existence of short codes with a given covering radius. In particular we show that there does not exist a code of codimension 11 and covering radius 2 which has length 64. We conclude with a table which gives the best available information for the length of a code with codimension m and covering radius r for 2 ≤ m ≤ 24 and 2 ≤ r ≤ 24.
*Research partially supported by National Science Foundation Grant No. DMS-8421521
Research partially supported by National Security Agency Grant No. MDA 904-85-H-0016
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. Ashlock. private communication.
R.A. Brualdi, V.S. Pless and R.M. Wilson, Short codes with a given covering radius, IEEE Trans. Inform. Theory (to appear).
A.R. Calderbank and N.J.A. Sloane, Inequalities for covering codes, preprint.
G.D. Cohen, M.G. Karpovsky, H.F. Mattson, Jr., and J.R. Schatz, Covering radius - survey and recent results, IEEE Trans. Inform. Theory, IT-31 (1985), pp. 328–343.
R.L. Graham and N.J.A. Sloane, On the covering radius of codes, IEEE Trans. Inform. Theory, IT-31 (1985), pp. 385–401.
R. Kibler. private communication
J. Simonis, The minimal covering radius t[15,6] of a 6-dimensional binary linear code of length 15 is equal to 4, preprint.
G.J.M. van Wee, Improved sphere bounds on the covering radius of codes, preprint.
I.S.Honkala, Modified bounds for covering codes, preprint.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag New York, Inc.
About this paper
Cite this paper
Brualdi, R.A., Pless, V.S. (1990). On the Length of Codes with a Given Covering Radius. In: Coding Theory and Design Theory. The IMA Volumes in Mathematics and Its Applications, vol 20. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8994-1_2
Download citation
DOI: https://doi.org/10.1007/978-1-4613-8994-1_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-8996-5
Online ISBN: 978-1-4613-8994-1
eBook Packages: Springer Book Archive