Algebraic geometry codes of curves of complete intersection (Q1337378)

A class of algebraic geometric codes is constructed on curves of complete intersection in \(P_q^3\) (projective 3-space over \(\mathrm{GF}(q))\). By restricting to this class of curves, the author is able to derive estimates for the rate and minimum distance of the corresponding codes and their duals. In particular, the parameters of the code and dual code determined by \(y^3 - yw^2 - z^2x = x^2 - zx = 0\) over \(\mathrm{GF}(81)\) are given. A decoding algorithm is presented for this class of codes which is a generalization of Peterson's algorithm for decoding Reed-Solomon codes. In special cases this ``generalized Peterson algorithm'' can be used to correct at most \(\frac{d^*} {2}\) errors, where \(d^*\) is the design distance of the code.