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

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1199-1202
Number of pages	4
Journal	IEEE Transactions on Information Theory
Volume	51
Issue number	3
DOIs	https://doi.org/10.1109/TIT.2004.842740
Publication status	Published - Mar 2005
Externally published	Yes

Keywords

Characteristic generators
Characteristic matrices
Conventional trellises
Cyclic codes
Tailbiting trellises

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10.1109/TIT.2004.842740

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

Abstract

Keywords

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