Two classes of cyclic extended double-error-correcting goppa codes

Let F-2m be a finite extension of the field F-2 and g(x) = x(2) +alpha x+ 1 a quadratic polynomial over F-2m . In this paper, two classes of cyclic extended double-error-correcting Goppa codes are proposed. We obtain the following two classes of Goppa codes: (1) cyclic extended Goppa code with the irreducible polynomial g(x) and L = F-2m boolean OR {infinity}; (2) cyclic extended Goppa code with the reducible polynomial g(x) and vertical bar L'vertical bar = 2(m) - 1. In addition, the parameters of above cyclic extended Goppa codes are given.