Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds improve on the best known analytic bounds. Several new record bounds are obtained for codes with small lengths

The main purpose of this paper is to give bounds on the length of the shortest and longest binary quasi-perfect codes with a given Hamming distance, covering radius, and redundancy. We consider codes with Hamming distance 4 and 5 and covering radius 2 and 3, respectively. We discuss the blockwise direct sum (BDS) construction which has an important role in finding these bounds.

The main purpose of this paper is to give bounds on the length of the shortest and longest binary quasiperfect codes with a given Hamming distance, covering radius, and redundancy. We consider codes with Hamming distance 4 and 5 and covering radius 2 and 3, respectively.

Let A(n,d) denote the maximum possible number of codewords in a binary code of length n and minimum Hamming distance d. For large values of n, the best known upper bound, for fixed d, is the Johnson bound. We give a new upper bound which is at least as good as the Johnson bound for all values of n and d, and for each d there are infinitely many values of n for which the new bound is better than the Johnson bound. For small values of n and d, the best known method to obtain upper bounds on A(n,d) is linear programming. We give new inequalities for the linear programming and show that with these new inequalities some of the known bounds on A(n,d) for n/spl les/28 are improved.