On Z2Z4-additive complementary dual codes and related LCD codes |
| |
| Institution: | 1. Faculty of Mathematics, University of Science and Technology Houari Boumediene, Algeria;2. Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, Spain;3. Department of Mathematics, University of Scranton, United States of America;1. Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China;2. PCL Research Center of Networks and Communications, Peng Cheng Laboratory, Shenzhen 518055, China;3. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China;4. Tianjin Key Laboratory of Network and Data Security Technology, Nankai University, Tianjin 300071, China;1. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China;2. State Key Laboratory of Cryptology, P.O. Box 5159, Beijing 100878, China;1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, PR China;2. State Key Laboratory of Cryptology, P. O. Box 5159, Beijing, 100878, PR China;3. Department of Mathematics, Ewha Womans University, Seoul, 03760, South Korea;1. IMDEA Software Institute, Madrid, Spain;2. Department of Mathematical Sciences, Aalborg University, Denmark;3. IMUVA-Mathematics Research Institute, Universidad de Valladolid, Spain |
| |
| Abstract: | Linear complementary dual codes were defined by Massey in 1992, and were used to give an optimum linear coding solution for the two user binary adder channel. In this paper, we define the analog of LCD codes over fields in the ambient space with mixed binary and quaternary alphabets. These codes are additive, in the sense that they are additive subgroups, rather than linear as they are not vector spaces over some finite field. We study the structure of these codes and we use the canonical Gray map from this space to the Hamming space to construct binary LCD codes in certain cases. We give examples of such binary LCD codes which are distance-optimal, i.e., they have the largest minimum distance among all binary LCD codes with the same length and dimension. |
| |
| Keywords: | LCD codes Complementary dual Gray map |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
