Improved geometric Goppa codes
G.L. Feng, T.R.N. Rao, Lloyd R. Welch · 2002
Summary form only given. A new class of geometric Goppa codes are discussed. We show that the improved geometric Goppa codes are more efficient than the current geometric Goppa codes, for many cases. We also show several improved geometric Goppa codes from algebraic curves in high-dimensional spaces, hyperplanes in affine spaces and projective spaces, surfaces in affine spaces, and some varieties generated by algebraic curves. As special cases, the multi-level codes derived by Wu and Costello (see IEEE Trans. Information Theory, vol.IT-38, p.933, 1992), the hyperbolic cascaded Reed-Solomon codes derived by Saints and Heegard (see Lecture Notes in Computer Science 673, p.291, 1993), Chen (1986) codes, and their generalizations can be easily derived.>