IMPROVED GEOMETRIC GOPPA CODES .1. BASIC THEORY

In this paper, we present a construction of improved geometric Goppa c odes which, for the case of r<2g, are often more efficient than the cu rrent geometric Goppa codes derived from some varieties, which include algebraic curves, hyperplanes, surfaces, and other varieties. For the special case of a plane in a three-dimensional projective space, the improved geometric Goppa codes are reduced to linear multilevel codes. For these improved geometric Goppa codes, a designed minimum distance can be easily determined and a decoding procedure which corrects up t o half the designed minimum distance is also given.