Nonexistence of some four dimensional linear codes attaining the Griesmer bound
Wen Ma, Jinquan Luo · Advances in Mathematics of Communications · 2023
In coding theory, it is important to construct codes with optimal parameters. The codes meeting the Griesmer bound are called Griesmer codes. In this paper, we prove nonexistence of some Griesmer codes of dimension four over finite fields of cardinality eight and nine using projective geometry. Moreover, we improve 24 cases on code lengths for given minimal distance and dimension four. Two precise lower bounds of code lengths have also been determined.