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Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 42, No. 2, pp. 601-611 (2001)
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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; e-mail: Joern.Quistorff@Hamburg.de

**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 existence problem is presented by using a multiple covering of the farthest-off points.

** Editorial Remark:** This article replaces the version published by the same author in Beiträge zur Algebra und Geometrie 41, No. 2, 469-478 (2000). Due to an error in the files transmission the publication of that version was not based on the final TEX-file for the article. Hence some improvements suggested by the referee were missing.

**Full text of the article:**

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