An optimal ternary [69, 5, 45] code and related codes

M.J.M. Eupen, van; R. Hill

doi:10.1007/BF01388456

An optimal ternary [69, 5, 45] code and related codes

M.J.M. Eupen, van, R. Hill

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

24 Citations (Scopus)

Abstract

A ternary [69, 5, 45] code is constructed, thus solving the problem of finding the minimum length of a ternary code of dimension 5 and minimum distance 45. Furthermore, this code is shown to be a unique two-weight code with weight enumerator 1+210Z45+32Z54. It is also shown that a ternary [70, 6, 45] code, which would have been a projective two-weight code giving rise to a new strongly regular graph, does not exist. In order to prove the main results, the uniqueness of some other optimal ternary codes with specified weight enumerators is also established.

Original language	English
Pages (from-to)	271-282
Number of pages	12
Journal	Designs, Codes and Cryptography
Volume	4
Issue number	4
DOIs	https://doi.org/10.1007/BF01388456
Publication status	Published - 1994

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abstract = "A ternary [69, 5, 45] code is constructed, thus solving the problem of finding the minimum length of a ternary code of dimension 5 and minimum distance 45. Furthermore, this code is shown to be a unique two-weight code with weight enumerator 1+210Z45+32Z54. It is also shown that a ternary [70, 6, 45] code, which would have been a projective two-weight code giving rise to a new strongly regular graph, does not exist. In order to prove the main results, the uniqueness of some other optimal ternary codes with specified weight enumerators is also established.",

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AB - A ternary [69, 5, 45] code is constructed, thus solving the problem of finding the minimum length of a ternary code of dimension 5 and minimum distance 45. Furthermore, this code is shown to be a unique two-weight code with weight enumerator 1+210Z45+32Z54. It is also shown that a ternary [70, 6, 45] code, which would have been a projective two-weight code giving rise to a new strongly regular graph, does not exist. In order to prove the main results, the uniqueness of some other optimal ternary codes with specified weight enumerators is also established.

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DO - 10.1007/BF01388456

M3 - Article

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JO - Designs, Codes and Cryptography

JF - Designs, Codes and Cryptography

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ER -

An optimal ternary [69, 5, 45] code and related codes

Abstract

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