A relation between the characteristic generators of a linear code and its dual

Haibin Kan; Hong Shen

doi:10.1109/TIT.2004.842740

A relation between the characteristic generators of a linear code and its dual

Haibin Kan
, Hong Shen

研究成果: Article › 同行評審

21 引文斯高帕斯（Scopus）

摘要

It was conjectured by Koetter and Vardy that if the k characteristic generators of a linear code C are linearly independent, then the corresponding n - k characteristic generators of the dual code C^⊥ are also linearly independent. In this correspondence, we prove that the conjecture is true for self-dual codes and cyclic codes.

原文	English
頁（從 - 到）	1199-1202
頁數	4
期刊	IEEE Transactions on Information Theory
卷	51
發行號	3
DOIs	https://doi.org/10.1109/TIT.2004.842740
出版狀態	Published - 3月 2005
對外發佈	是

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abstract = "It was conjectured by Koetter and Vardy that if the k characteristic generators of a linear code C are linearly independent, then the corresponding n - k characteristic generators of the dual code C⊥ are also linearly independent. In this correspondence, we prove that the conjecture is true for self-dual codes and cyclic codes.",

keywords = "Characteristic generators, Characteristic matrices, Conventional trellises, Cyclic codes, Tailbiting trellises",

author = "Haibin Kan and Hong Shen",

note = "Funding Information: Manuscript received September 19, 2003; revised October 26, 2004. This work was supported by the National Science Foundation of China under Grants 60003007 and 60472038 and by the Japan Society for Promotion of Science (JSPS) under Research Grant 14380139.",

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AU - Shen, Hong

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N2 - It was conjectured by Koetter and Vardy that if the k characteristic generators of a linear code C are linearly independent, then the corresponding n - k characteristic generators of the dual code C⊥ are also linearly independent. In this correspondence, we prove that the conjecture is true for self-dual codes and cyclic codes.

AB - It was conjectured by Koetter and Vardy that if the k characteristic generators of a linear code C are linearly independent, then the corresponding n - k characteristic generators of the dual code C⊥ are also linearly independent. In this correspondence, we prove that the conjecture is true for self-dual codes and cyclic codes.

KW - Characteristic generators

KW - Characteristic matrices

KW - Conventional trellises

KW - Cyclic codes

KW - Tailbiting trellises

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JF - IEEE Transactions on Information Theory

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A relation between the characteristic generators of a linear code and its dual

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