Improved Power Decoding of One-Point Hermitian Codes

TL;DR

This paper introduces a new partial decoding algorithm for one-point Hermitian codes that matches the error-correcting capability of the Guruswami--Sudan decoder, with similar failure probability and computational advantages.

Contribution

It presents a novel decoding algorithm based on a generalization of power decoding for Reed--Solomon codes, eliminating the need for root-finding and improving decoding of interleaved Hermitian codes.

Findings

Decodes up to the same errors as Guruswami--Sudan decoder.

Has similar failure probability to Guruswami--Sudan decoder.

Potential improvements for decoding interleaved Hermitian codes.

Abstract

We propose a new partial decoding algorithm for one-point Hermitian codes that can decode up to the same number of errors as the Guruswami--Sudan decoder. Simulations suggest that it has a similar failure probability as the latter one. The algorithm is based on a recent generalization of the power decoding algorithm for Reed--Solomon codes and does not require an expensive root-finding step. In addition, it promises improvements for decoding interleaved Hermitian codes.