On epicyclic Hermitian codes

The class of Hermitian codes is a popular and well-studied class of codes on planar curves over GF(2^m). These codes have large blocklength, and may soon find engineering importance. In contrast to Reed-Solomon codes, which were discovered by engineers, Hermitian codes were introduced by mathematicians as an example of algebraic geometry codes. We re-introduce Hermitian codes as if they had been discovered by the engineering community. Many insights emerge from this development. In particular, we give constructions of Hermitian codes as quasi cyclic codes and as linear combinations of Reed-Solomon codes akin to the Turyn construction