2007/12/11 by Rachit Agarwal, Agarwal, Rachit
Computer Science · Mathematics · #Coding theory and cryptography #Cryptographic Implementations and Security #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.0712.1775
10 pages, Submitted to ITW 2008 (with some minor modifications)
arxiv created 2007/12/11 · openalex publication_date 2007/12/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We obtain a technique to reduce the computational complexity associated with decoding of Hermitian codes. In particular, we propose a method to compute the error locations and values using an uni-variate error locator and an uni-variate error evaluator polynomial. To achieve this, we introduce the notion of Semi-Erasure Decoding of Hermitian codes and prove that decoding of Hermitian codes can always be performed using semi-erasure decoding. The central results are: * Searching for error locations require evaluating an univariate error locator polynomial over q2 points as in Chien search for Reed-Solomon codes. * Forney's formula for error value computation in Reed-Solomon codes can directly be applied to compute the error values in Hermitian codes. The approach develops from the idea that transmitting a modified form of the information may be more efficient that the information itself.