On the minimum length of quaternary linear codes of dimension five

Ivan N. Landjev, Tatsuya Maruta
1999 Discrete Mathematics  
Let n,(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 n4(5,d) for d = 141,142 and determines the exact value of n4(5,d) for d = 178, 205, 206, 215, 217, 218, 365, 366, 367, 368. The updated table of ~(5, d) is also given.
doi:10.1016/s0012-365x(98)00354-9 fatcat:cw6g35whsjfyzmog22o2clxtby