Construction of quasi-cyclic self-dual codes |
| |
Authors: | Sunghyu Han Jon-Lark Kim Heisook Lee Yoonjin Lee |
| |
Institution: | 1. School of Liberal Arts, Korea University of Technology and Education, Cheonan 330-708, South Korea;2. Department of Mathematics, University of Louisville, Louisville, KY 40292, USA;3. Department of Mathematics, Ewha Womans University, Seoul 120-750, South Korea |
| |
Abstract: | There is a one-to-one correspondence between ?-quasi-cyclic codes over a finite field and linear codes over a ring . Using this correspondence, we prove that every ?-quasi-cyclic self-dual code of length m? over a finite field can be obtained by the building-up construction, provided that or , m is a prime p, and q is a primitive element of . We determine possible weight enumerators of a binary ?-quasi-cyclic self-dual code of length p? (with p a prime) in terms of divisibility by p. We improve the result of Bonnecaze et al. (2003) 3] by constructing new binary cubic (i.e., ?-quasi-cyclic codes of length 3?) optimal self-dual codes of lengths (Type I), 54 and 66. We also find quasi-cyclic optimal self-dual codes of lengths 40, 50, and 60. When , we obtain a new 8-quasi-cyclic self-dual code over and a new 6-quasi-cyclic self-dual code over . When , we find a new 4-quasi-cyclic self-dual code over and a new 6-quasi-cyclic self-dual code over . |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|