• 中国计算机学会会刊
  • 中国科技核心期刊
  • 中文核心期刊

J4 ›› 2015, Vol. 37 ›› Issue (09): 1661-1666.

• 论文 • 上一篇    下一篇

有19-(4,f)型自同构的二元自对偶码

王荣,王俊新   

  1. (山西财经大学应用数学学院,山西 太原 030006)
  • 收稿日期:2014-12-17 修回日期:2015-04-21 出版日期:2015-09-25 发布日期:2015-09-25
  • 基金资助:

    国家自然科学基金资助项目(70973072,70573066);山西财经大学青年科研基金资助项目(晋财大校[2014]90号)

Binary self-dual codes with 19-(4,f)  automorphism  

 WANG Rong,WANG Junxin   

  1. (College of Applied Mathematics,Shanxi University of Finance and Economics,Taiyuan 030006,China )
  • Received:2014-12-17 Revised:2015-04-21 Online:2015-09-25 Published:2015-09-25

摘要:

应用二元自对偶码可看成几个自对偶码的直和理论,研究了具有19(4,f)型自同构、码长在100以内的的二元自对偶码。这种对偶码都可看成一个码长为4的收缩码和GF(2)n上一些偶重量多项式的直和。证明了码长大于80且小于100时,不存在19(4,f)型的二元自对偶码。根据码长较短的自对偶码分别构造出了码长为76、78和80的二元自对偶码,并给出其生成矩阵。由码的等价得到了这几类码可能的分类情况。运行Matlab程序,证明了具有19(4,2)型和19(4,4)型的二元自对偶码在等价情况下都有11个,19(4,0)型的二元自对偶码在等价情况下是不存在的。

关键词: 自对偶码, 生成矩阵, 自同构, 等价

Abstract:

We discuss the binary selfdual codes of length 76 and 100 with automorphism of order 19. These binary selfdual codes can be seen as a direct sum of contract code of length 4 and some evenweight polynomials over  GF(2)n. We prove that selfdual codes of length between 80 and 100 do not exist. We also construct the binary selfdual codes of length 76, 78 and 80 through the shorter selfdual codes respectively, and present their generator matrices. Simulations in Matlab prove that under the condition of equivalence, there are 11 binary selfdual codes of 19(4, 2) and 19(4,4) types, whereas binary selfdual codes of 19(4, 0) type do not exist.

Key words: self-dual codes;generator matrix;automorphism;equivalence