A New Construction of Block Codes From Algebraic Curves

Since discovery of Goppa geometric codes, people have been asking the question: are there different constructions of block codes from algebraic curves that give the same parameters as Goppa geometric codes. Despite of great effort by researchers, no such constructions have been found so far. Although in literature, there are many constructions of block code from algebraic curves, most of them are quite different from the one by Goppa in nature and thus they have different parameters. Some of these constructions have the same parameters as Goppa geometric codes, however it was proved that these are essentially the same codes defined by Goppa. In this paper, we solve this question for the case where the characteristic of the ground field is 2, namely, we present a different construction of block codes from algebraic curves that give the same parameters as Goppa geometric codes for the characteristic 2 case.