On the minimum length of linear codes over F5F5

We construct a lot of new [n,5,d]5[n,5,d]5 codes close to the Griesmer bound and prove the nonexistence of some Griesmer codes to determine the exact value of n5(5,d)n5(5,d) or to improve the known upper bound on n5(5,d)n5(5,d), where nq(k,d)nq(k,d) is the minimum length nn for which an [n,k,d]q[n,k,d]q code exists. We also give the updated table for n5(5,d)n5(5,d) for all dd except some known cases.