A simple proof of the formal duality of the Kerdock and Preparata codes

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	A simple proof of the formal duality of the Kerdock and Preparata codes
	Wan, ZX
	2000-07-01
发表期刊	CHINESE SCIENCE BULLETIN
ISSN	1001-6538
卷号	45 期号:14 页码:1279-1282
摘要	The nonlinearity of the Z(2)-Kerdock code Km+1, where m is an odd integer greater than or equal to 3, is not at all obvious. By regarding Km+1 as the binary image of the Z(4)-Kerdock code K(m) under the Gray map([1]), a simple proof can be achieved (cf. Theorems 8.7 and 8.9 of [2]). Similarly, the formal duality of the Z(2)-Kerdock code Km+1 and the Z(2)-Preparata code Pm+1 is even more not at all obvious. A simple proof is given in the present note, by regarding Km+1 as the binary image of K (m) and using the duality of k(m) and the Z(4)-Preparata code P(m) established in [1].
关键词	Z(4)-code Kerdock code Preparata code formal duality
语种	英语
WOS研究方向	Science & Technology - Other Topics
WOS类目	Multidisciplinary Sciences
WOS记录号	WOS:000089246900006
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/15557
专题	中国科学院数学与系统科学研究院
通讯作者	Wan, ZX
作者单位	Chinese Acad Sci, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Wan, ZX. A simple proof of the formal duality of the Kerdock and Preparata codes[J]. CHINESE SCIENCE BULLETIN,2000,45(14):1279-1282.
APA	Wan, ZX.(2000).A simple proof of the formal duality of the Kerdock and Preparata codes.CHINESE SCIENCE BULLETIN,45(14),1279-1282.
MLA	Wan, ZX."A simple proof of the formal duality of the Kerdock and Preparata codes".CHINESE SCIENCE BULLETIN 45.14(2000):1279-1282.