Nonexistence of some Griesmer codes over FqFq

We prove the nonexistence of [gq(4,d),4,d]q[gq(4,d),4,d]q codes for d=q3/2−q2−2q+1d=q3/2−q2−2q+1 for q=2hq=2h, h≥3h≥3, and for d=2q3−3q2−2q+1d=2q3−3q2−2q+1 for q≥5q≥5, where gq(k,d)=∑i=0k−1⌈d/qi⌉. We also prove the nonexistence of [gq(k,d),k,d]q[gq(k,d),k,d]q code for d=(k−2)qk−1−rqk−2−q+1d=(k−2)qk−1−rqk−2−q+1 for 3≤k−1≤r≤q−q/p3≤k−1≤r≤q−q/p, q=phq=ph with pp prime.