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In this article we improve the lower bound for K 2 (9, 1), the minimum cardinality of a binary code of length 9 and covering radius 1. We show that a binary code of length 9, 55 codewords and covering radius 1 does not exist which gives a new lower bound K 2 (9, 1) >= 56.
A group divisible covering design (GDCD) with block size k and group-type g u is defined to be a triple (X, G, B) where X is a gu-set (of points), G is a partition of X into g-subsets (called groups), B is a set of k-subsets of X (called blocks) such that a group and a block contain at most one common point and every pair of points from distinct groups occurs in at least one block. The covering...
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