On the Nonexistence of Some Griesmer Codes with Dimension Four

In coding theory, it is important to construct codes meeting certain types of bounds. The codes meeting the Griesmer bound are called Griesmer codes. In this paper, we prove the nonexistence of some Griesmer codes of dimension four over finite fields of cardinality eight and nine. Moreover, we improve 24 cases on code lengths for given minimal distance and dimension 4. Two cases on precise lower bound of code lengths have also been determined.