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Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 41, No. 2, pp. 469-478 (2000)
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On Codes with Given Minimum Distance and Covering Radius

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Jörn Quistorff

Speckenreye 48, D-22119 Hamburg, Germany

**Abstract:** Codes with minimum distance at least $d$ and covering radius at most $d-1$ are considered. The minimal cardinality of such codes is investigated. Herewith, their connection to covering problems is applied and a new construction theorem is given. Additionally, a new lower bound for the covering problem is proved. A necessary condition on an existance problem is presented by using a multiple covering of the farthest-off points.

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