We prove the nonexistence of binary [69,9,32] codes and construct codes with parameters [76,9,34],[297,9,146], and [300,9,148]. These results show that n(9,32)=70, n(9,34)/spl les/76,n(9,146)=297, and n(9,148)=300, where n(k,d) denotes the smallest value of n for which there exists an [n,k,d] binary code. We also present some codes of minimum distance 32 and some related codes.

Let n(k, d) be the smallest integer n for which a binary linear code of length n, dimension k, and minimum distance d exists. Using the residual code technique, the MacWilliams identities and the weight distribution of appropriate Reed-Muller codes, we prove that n(9, 64)=133, n(9, 120)/spl ges/244, n(9, 124)=252, and n(9, 184)=371. We also show that puncturing a known [322, 9, 160]-code yields length-optimal codes with parameters [319, 9, 158], [315, 9, 156], and [312, 9, 154].