首页 | 本学科首页   官方微博 | 高级检索  
     


Homogeneous metric and matrix product codes over finite commutative principal ideal rings
Affiliation:1. Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta, T1K 3M4, Canada;2. Department of Mathematics, National Defense Academy of Japan, Yokosuka, Kanagawa, 239-8686, Japan;1. Instituto Universitario de Matemáticas y Aplicaciones de Castellón and Departamento de Matemáticas, Universitat Jaume I, Campus de Riu Sec. 12071 Castelló, Spain;2. Instituto de Matemáticas (Imuva) and Departamento de Matemática Aplicada, Universidad de Valladolid, Avda Salamanca SN, 47014 Valladolid, Spain;1. Department of Mathematics, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic;2. Institut de Mathématiques de Toulon, campus La Garde, 83041 Toulon, France;1. College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, China;2. School of Mathematics and Statistics, Hunan University of Technology and Business, Changsha, China;3. State Key Laboratory of Cryptology, Beijing, 100878, China
Abstract:In this paper, a necessary and sufficient condition for the homogeneous distance on an arbitrary finite commutative principal ideal ring to be a metric is obtained. We completely characterize the lower bound of homogeneous distances of matrix product codes over any finite principal ideal ring where the homogeneous distance is a metric. Furthermore, the minimum homogeneous distances of the duals of such codes are also explicitly investigated.
Keywords:Matrix product codes  Homogeneous distances  Finite commutative principal ideal rings  Dual codes
本文献已被 ScienceDirect 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号