On optimal linear codes over F5

Let nq(k,d) be the smallest integer n for which there exists a linear code of length n, dimension k and minimum distance d over Fq, the field of q elements. We determine n5(5,d) for d=476-479, 491-530, 538-540, 542-560, 563-625. We also show that n5(5,d)≥g5(5,d)+1 for d=70-120, 144-150, 268-275, 280-290, 293-300, 394, 395, 398-400 and that n5(5,d)≥g5(5,d)+2 for d=373-375 and so on, where gq(k,d)=∑i=0k−1⌈d/qi⌉.