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	Johnson type bounds on constant dimension codes
	Xia, Shu-Tao ; Fu, Fang-Wei
	2010-10-12 ; 2010-10-12
关键词	Constant dimension codes Linear authentication codes Binary constant weight codes Johnson bounds Steiner structures Random network coding Computer Science, Theory & Methods Mathematics, Applied
中文摘要	Very recently, an operator channel was defined by Koetter and Kschischang when they studied random network coding. They also introduced constant dimension codes and demonstrated that these codes can be employed to correct errors and/or erasures over the operator channel. Constant dimension codes are equivalent to the so-called linear authentication codes introduced by Wang, Xing and Safavi-Naini when constructing distributed authentication systems in 2003. In this paper, we study constant dimension codes. It is shown that Steiner structures are optimal constant dimension codes achieving the Wang-Xing-Safavi-Naini bound. Furthermore, we show that constant dimension codes achieve the Wang-Xing-Safavi-Naini bound if and only if they are certain Steiner structures. Then, we derive two Johnson type upper bounds, say I and II, on constant dimension codes. The Johnson type bound II slightly improves on the Wang-Xing-Safavi-Naini bound. Finally, we point out that a family of known Steiner structures is actually a family of optimal constant dimension codes achieving both the Johnson type bounds I and II.
语种	英语 ; 英语
出版者	SPRINGER ; DORDRECHT ; VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/81759]
专题	清华大学
推荐引用方式 GB/T 7714	Xia, Shu-Tao,Fu, Fang-Wei. Johnson type bounds on constant dimension codes[J],2010, 2010.
APA	Xia, Shu-Tao,&Fu, Fang-Wei.(2010).Johnson type bounds on constant dimension codes..
MLA	Xia, Shu-Tao,et al."Johnson type bounds on constant dimension codes".(2010).

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