On the minimum length of quaternary linear codes of dimension five

Let n(q)(k,d) be the smallest integer n for which there exists a linear code of length n, dimension k and minimum distance d, over the q-element field. In this paper we prove the nonexistence of quaternary linear codes with parameters [190,5,141], [239,5,178], [275,5,205], [288,5,215], [291,5,217] and [488,5,365]. This gives an improved lower bound of n(4)(5,d) for d = 141,142 and determines the exact value of n(4)(5,d) for d = 178, 205, 206, 215, 217, 218, 365, 366, 367, 368. The updated table of n(4)(5,d) is also given. (C) 1999 Elsevier Science B.V. All rights reserved.