Algebraic-geometric codes on the erasure channel

This paper investigates the use of algebraic-geometric codes for data transmission over a packet network, by comparing their encoding/decoding speeds to those of the ubiquitous Reed-Solomon Codes. We take advantage of the fact that AG codes allow the construction of longer codes over a given alphabet, which in turn means we can create an [n, k]-code over a smaller field in which the encoding/decoding algorithms run faster. We also obtain some probabilistic bounds on the overheads required for the codes we use.