On Computation of Error Locations and Values in Hermitian Codes
Abstract
Description
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.
10 pages, Submitted to ITW 2008 (with some minor modifications)
10 pages, Submitted to ITW 2008 (with some minor modifications)