On the [162, 8, 80] codes

Constructions of 162,8,80] and 159,8,78] codes are given. This solves the open problems of nding the minimum length of binary codes of dimension 8 and minimum distances 78 and 80 respectively. 1 Introduction Let F n q be the n-dimensional vector space over the Galois eld F q. The Hamming distance between two vectors of F n q is deened to be the number of coordinates in which they diier. In this paper, we shall connne ourselves to the case of q = 2. A (binary) linear n; k; d] code is a k-dimensional linear subspace of F n 2 with minimum distance d. Let n(k; d) denote the smallest value of n for which there exists an n; k; d] code. Baumert and McEliece 1] determined n(k; d) for k 6, van Tilborg 19] completed the case k = 7.