Let m be a positive integer and F2m be a finite field.A binary Goppa code Γ(L,G)is specified by a separable Goppa polynomial G(x)=x3t+1 and a locator set L of elements of F2m,where no elements of L may be a root of G(x)and t|(2m-1).For the nontrivial code,we prove that its minimum distance is equal to the design distance,namely d=6t+1.This extends a result of Bezzateev and Shekunova(1995).We also present many new binary linear codes,which extend the codetable of Grassl as a byproduct.It is worth emphasizing that we have identified at least three binary linear codes with parameters[32,16,8],[62,43,8],and[128,106,8],respectively.These codes are considered the best-known linear codes with these specific parameters and are not equivalent to any codes with the same parameters listed in the Grassl's codetable.
万方数据