Improved power decoding of interleaved one-point Hermitian codes

作     者：Puchinger, Sven Rosenkilde, Johan Bouw, Irene 

作者机构：Tech Univ Munich Inst Commun Engn Munich Germany Tech Univ Denmark Dept Appl Math & Comp Sci Lyngby Denmark Ulm Univ Inst Pure Math Ulm Germany 

出 版 物：《DESIGNS CODES AND CRYPTOGRAPHY》 (设计、编码与密码学)

年 卷 期：2019年第87卷第2-3期

页      面：589-607页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：We would like to thank the anonymous reviewers for their helpful comments  which improved the readability of the paper 

主　　题：Interleaved one-point Hermitian codes Power decoding Collaborative decoding 

摘      要：An h-interleaved one-point Hermitian code is a direct sum of h many one-point Hermitian codes, where errors are assumed to occur at the same positions in the constituent codewords. We propose a new partial decoding algorithm for these codes that can decodeunder certain assumptionsan error of relative weight up to 1-(, where k is the dimension, n the length, and g the genus of the code. Simulation results for various parameters indicate that the new decoder achieves this maximal decoding radius with high probability. The algorithm is based on a recent generalization of improved power decoding to interleaved Reed-Solomon codes, does not require an expensive root-finding step, and improves upon the previous best decoding radius at all rates. In the special case h=1, we obtain an adaption of the improved power decoding algorithm to one-point Hermitian codes, which for all simulated parameters achieves a similar observed failure probability as the Guruswami-Sudan decoder above the latter s guaranteed decoding radius.