Trellis complexity and pseudoredundancy of relative two-weight codes

作     者：Liu, Zihui Wu, Xin-Wen 

作者机构：Beijing Inst Technol Dept Math Beijing 100081 Peoples R China Griffith Univ Sch Informat & Commun Technol Gold Coast Qld 4222 Australia 

出 版 物：《APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING》 (工程、通信与计算应用代数)

年 卷 期：2016年第27卷第2期

页      面：139-158页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：National Science Foundation of China [11171366  61170257] 

主　　题：Relative two-weight code Separating property Trellis complexity Pseudocodeword Pseudoredundancy 

摘      要：Relative two-weight codes have been studied due to their applications to wiretap channel and secret sharing. It has been shown that these codes form a large family, which includes dual Hamming codes and subcodes of punctured Reed-Muller codes as special instances. This work studies the properties of relative two-weight codes with regard to efficient decoding. More specifically, the trellis complexity, which determines the complexity of Viterbi algorithm based decoding and pseudoredundancy that measures the performance and complexity of linear programming decoding are studied for relative two-weight codes. Separating properties of these codes have been identified and proved first. Based on the results of separating properties, the trellis complexity of binary relative two-weight codes is fully determined. An upper bound on the pseudoredundancy of binary relative two-weight codes is derived.