Architectures for syndrome generation and error-location search in the decoding of Hermitian codes

摘要

When a Hermitian curve is put in a special position with respect to its infinite rational point, the (x, y) coordinates of all its finite rational points have regular algebraic properties. Based on these properties, the use of Horner's rule and the mechanism of Chien search in the decoding of Reed-Solomon codes can be extended to render architectures for syndrome generation and error-location search in the decoding of codes constructed from the Hermitian curve.