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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