Construction of Improved Geometric Goppa Codes from Klein Curves and Klein-like Curves

Abstract

Linear error-correcting codes, especially Reed-Solomon codes, find applications in communication and computer memory systems, to enhance their reliability and data integrity. In this paper, we present Improved Geometric Goppa (IGG) codes, a new class of error-correcting codes, based on the principles of algebraic-geometry. We also give a reasonably low complexity procedure for the construction of these IGG codes from Klein curves and Klein-like curves, in plane and high-dimensional spaces. These codes have good code parameters like minimum distance rate and information rate, and have the potential to replace the conventional Reed-Solomon codes in most practical applications. Based on the approach discussed in this paper, it might be possible to construct a class of codes whose performance exceeds the Gilbert-Varshamov bound.