Performance comparison of Hermitian and Reed-Solomon codes

This paper compares the performance of low and high-rate Reed-Solomon codes with Hermitian codes, that is, algebraic-geometric codes based on Hermitian curves, over fields containing 16, 64, 256, 512, and 4096 elements. Comparisons of Reed-Solomon codes with much longer Hermitian codes over the same field demonstrate the utility of Hermitian codes with respect to the trade-off between coding gain and bandwidth expansion. Comparisons of Reed-Solomon and Hermitian codes of the same length, but over different fields, show an increasingly favorable trade-off between bandwidth expansion and complexity of finite-field arithmetic computations as code length increases.