Abstract
We give a table with the most current available information for the shortest length of a binary code with codimension m and covering radius r for 2≤m≤24 and 2≤r≤12.
This work was supported in part by NSA Grant MDA 904-91-H-0003.
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R.A. Brualdi, V.S. Hess, R.M. Wilson: Short codes with a given covering radius. IEEE IT-35, 99–109 (1989)
R.A. Brualdi, V.S. Pless: On the length of codes with a given covering radius. In: Coding Theory and Design Theory. Part I: Coding Theory. Springer-Verlag 1990, pp. 9–15
A.A. Davydov, A.Y. Drozhzhina-Labinskaya: Constructions, families and tables of binary linear covering codes. IEEE IT, to appear
R. Dougherty, H. Janwa: Covering radius computations for binary cyclic codes. Mathematics of Computation 57, 415–434 (1991)
R.L. Graham, N.J.A. Sloane: On the covering radius of codes. IEEE IT-31, 385–401 (1985)
X.D. Hou: Covering radius and error correcting codes. Ph. D. thesis, University of Illinois, Chicago 1990, 77 p.
X.D. Hou: New lower bounds for covering codes. IEEE IT-36, 895–899 (1990)
D. Li, W. Chen: New lower bounds for binary covering codes. IEEE IT, to appear
R. Struik: On the structure of linear codes with covering radius two and three. IEEE IT, submitted
R. Struik: An improvement of the van Wee bound for linear covering codes. IEEE IT, submitted
G.J.M. van Wee: Improved sphere bounds on the covering radius of codes. IEEE. IT-34, 237–245 (1988)
O. Ytrehus: Binary [18,11]2 codes do not exist — nor do [64,53]2 codes. IEEE IT-37, 349–351 (1991)
Z. Zhang, C. Lo: Lower bounds on t[n,k] from linear inequalities. IEEE IT-38, 194–197 (1992)
Z. Zhang, C. Lo: Linear inequalities for covering codes: Part II — triple covering inequalities. IEEE IT-38, 1648–1662 (1992)
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© 1994 Springer-Verlag Berlin Heidelberg
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Lobstein, A., Pless, V. (1994). The length function: A revised table. In: Cohen, G., Litsyn, S., Lobstein, A., Zémor, G. (eds) Algebraic Coding. Algebraic Coding 1993. Lecture Notes in Computer Science, vol 781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57843-9_7
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DOI: https://doi.org/10.1007/3-540-57843-9_7
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