Abstract
We discuss a connection between weighted coverings and packings, study perfect weighted coverings (PWC) with diameter one and determine all the pairs (m0,m1) for which there exists a perfect q-ary linear (m0,m1)-covering.
Résumé
Nous discutons des liens entre recouvrements et pavages pondérés, étudions les recouvrements pondérés parfaits de diamètre 1 et déterminons toutes les paires (m0,m1) pour lesquelles des (m0,m1) recouvrements q-aires parfaits linéaires existent.
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References
Cohen, G.D., S.N. Litsyn and H.F. Mattson, Jr.: Binary perfect weighted coverings, in: Sequences ‘81, Positano, 17–22 June 1991, Springer-Verlag Lecture Notes in Computer Science,to appear.
Cohen, G.D., S.N. Litsyn and H.F. Mattson, Jr.: On perfect weighted coverings with small radius, in: First French-Soviet Workshop in Algebraic Coding, Paris, 22–24 July 1991, Springer-Verlag Lecture Notes in Computer Science 573, Berlin–Heidelberg, 1992, 32–41.
Etzion, T. and G. Greenberg: Constructions for perfect mixed codes and other covering codes, IEEE Trans. Inform. Theory, to appear.
Hämäläinen, H.O., I.S. Honkala, M.K. Kaikkonen and S.N. Litsyn: Bounds for binary multiple coverings, Designs, Codes and Cryptography, to appear.
Hämäläinen, H.O., I.S. Honkala and S.N. Litsyn, Bounds for binary codes that are multiple coverings of the farthest-off points, in preparation.
Li, D. and W. Chen: New lower bounds for binary covering codes, IEEE Trans. Inform. Theory, submitted.
Östergard, P.R.J.: Further results on (k,t)-subnormal covering codes, IEEE Trans. Inform. Theory 38 (1992) 206–210.
van Wee, G.J.M., G.D. Cohen and S.N. Litsyn: A note on perfect multiple coverings of Hamming spaces, IEEE Trans. Inform. Theory 37 (1991) 678–682.
Zhang, Z., Linear inequalities for covering codes: part I–pair covering inequalities, IEEE Trans. Inform. Theory 37 (1991) 573–582.
Zhang, Z. and C. Lo, Linear inequalities for covering codes: part II–triple covering inequalities,“ IEEE Trans. Inform. Theory 38 (1992) 1648–1662.
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© 1993 Springer-Verlag Wien
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Cohen, G.D., Honkala, I.S., Litsyn, S.N. (1993). On Weighted Coverings and Packings with Diameter One. In: Camion, P., Charpin, P., Harari, S. (eds) Eurocode ’92. International Centre for Mechanical Sciences, vol 339. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2786-5_4
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DOI: https://doi.org/10.1007/978-3-7091-2786-5_4
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82519-8
Online ISBN: 978-3-7091-2786-5
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