An Analogue of the Z4-Goethals Code in Non-Primitive Length  

作　　者：ALAHMADI Adel ALHAZMI Husain ALI Shakir HELLESETH Tor HIJAZI Rola LI Chunlei SOLE Patrick 

机构地区：[1]Department of Mathematics,Faculty of Science,King Abdulaziz University,Jeddah,Saudi Arabia [2]Department of Mathematics,Faculty of Science,Rabigh Campus,King Abdulaziz University,Rabigh,Saudi Arabia [3]Department of Informatics,University of Bergen,Bergen,Norway [4]CNRS/LAGA,University Paris 8,93 526 Saint-Denis,France

出　　处：《Journal of Systems Science & Complexity》2017年第4期950-966,共17页系统科学与复杂性学报（英文版）

基　　金：supported by the Norwegian Research Council

摘　　要：This paper constructs a cyclic Z_4-code with a parity-check matrix similar to that of Goethals code but in length 2~m+ 1, for all m ≥ 4. This code is a subcode of the lifted Zetterberg code for m even. Its minimum Lee weight is shown to be at least 10, in general, and exactly 12 in lengths 33, 65. The authors give an algebraic decoding algorithm which corrects five errors in these lengths for m = 5, 6 and four errors for m > 6.

关 键 词：Cyclic codes Goethals code Z4-codes. 

分 类 号：O157.4[理学—数学]