A class of algebraic geometric codes from curves in high-dimensional projective spaces

Abstract

Most of the research work in the area of algebraic geometric (AG) codes deals with the construction of AG codes from plane algebraic geometric curves. But, some work pertains to the construction of the AG codes from non- planar algebraic geometric curves. However, longer AG codes must have relatively larger genus and should only be the codes constructed from non- planar curves. In this paper, we present a new construction of a class of AG codes from curves in high- dimensional projective spaces. For this construction, it is easy to determine the designed minimum distance and find the parity check matrix, and the decoding up to the designed minimum distance is fast. Furthermore, this approach can be easily understood by most engineers.