Subclass of binary Goppa codes with minimal distance equal to the design distance

Abstract

A subclass of binary Goppa codes specified by a separable polynomial G(x)=x/sup t/+A and a subset L of elements of GF(2/sup m/) (no element of L may be a root of G(x) and t|(2/sup m/-1), A is a tth power in {GF(2/sup m/)/{0}}, is studied. For such codes it is shown that their minimal distance is equal to the design distance d=2t+1.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>