Abstract
When a nontrivial permutation of a Hermitian code is given, the code will have a module structure over a polynomial ring of one variable. By exploiting the theory of Gröbner bases for modules, a novel and elegant systematic encoding scheme for Hermitian codes is proposed in [1]. The goal of this paper is to develop a serial-in-serial-out hardware architecture, similar to a classical cyclic encoder, for such a systematic encoding schemes and demonstrates that the complexity of this architecture is much less than that of the brute-force systematic encoding by matrix multiplication.