On Computation of Error Locations and Values in Hermitian Codes

Abstract

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 $q^2$ 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.