Some new results on the minimum length of binary linear codes of dimensionnine

Let n(k, d) be the smallest integer n for which a binary linear code of len ght n, dimension k, and minimum distance d exists. Using the residual code technique, the MacWilliams identities and the weight distribution of approp riate Reed-Muller codes, we prove that n(9, 64) = 133, n(9, 120) greater th an or equal to 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 para meters [319, 9, 158], [315, 9, 156], and [312, 9, 154].