Nonexistence of some linear codes over the field of order four

We consider the problem of determining n4(5,d), the smallest possible length n for which an [n,5,d]4 code of minimum distance d over the field of order 4 exists. We prove the nonexistence of [g4(5,d)+1,5,d]4 codes for d=31,47,48,59,60,61,62 and the nonexistence of a [g4(5,d),5,d]4 code for d=138 using the geometric method through projective geometries, where gq(k,d)=∑i=0k−1d∕qi. This yields to determine the exact values of n4(5,d) for these values of d. We also give the updated table for n4(5,d) for all d except some known cases.