Unique Decoding of Plane AG Codes via Interpolation

Identificador:  imarina:5128046

Handle: https://hdl.handle.net/20.500.11797/imarina5128046

Autores:  Lee, K; Bras-Amorós, M; O'Sullivan, ME

Resumen:
We present a unique decoding algorithm of algebraic geometry (AG) codes on plane curves, Hermitian codes in particular, from an interpolation point of view. The algorithm successfully corrects errors of weight up to half of the order bound on the minimum distance of the AG code. It is the first decoding algorithm to combine some features of the interpolation-based list decoding with the performance of the syndrome decoding with the majority voting scheme. The regular structure of the algorithm allows a straightforward parallel implementation.