A quasi-symmetric 2-(49,9,6) design

Masaaki Harada; Akihiro Munemasa

doi:10.1002/jcd.10007

A quasi-symmetric 2-(49,9,6) design

Masaaki Harada, Akihiro Munemasa

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

3 Citations (Scopus)

Abstract

Abstract: Huffman and Tonchev discovered four non-isomorphic quasi-symmetric 2-(49,9,6) designs. They arise from extremal self-dual [50,25,10] codes with a certain weight enumerator. In this note, a new quasi-symmetric 2-(49,9,6) design is constructed. This is established by finding a new extremal self-dual [50,25,10] code as a neighbor of one of the four extremal codes discovered by Huffman and Tonchev. A number of new extremal self-dual [50,25,10] codes with other weight enumerators are also found.

Original language	English
Pages (from-to)	173-179
Number of pages	7
Journal	Journal of Combinatorial Designs
Volume	10
Issue number	3
DOIs	https://doi.org/10.1002/jcd.10007
Publication status	Published - 2002 Dec 1
Externally published	Yes

Keywords

Extremal self-dual code
Neighbor
Quasi-symmetric design
Weight enumerator

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1002/jcd.10007

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abstract = "Abstract: Huffman and Tonchev discovered four non-isomorphic quasi-symmetric 2-(49,9,6) designs. They arise from extremal self-dual [50,25,10] codes with a certain weight enumerator. In this note, a new quasi-symmetric 2-(49,9,6) design is constructed. This is established by finding a new extremal self-dual [50,25,10] code as a neighbor of one of the four extremal codes discovered by Huffman and Tonchev. A number of new extremal self-dual [50,25,10] codes with other weight enumerators are also found.",

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AU - Harada, Masaaki

AU - Munemasa, Akihiro

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N2 - Abstract: Huffman and Tonchev discovered four non-isomorphic quasi-symmetric 2-(49,9,6) designs. They arise from extremal self-dual [50,25,10] codes with a certain weight enumerator. In this note, a new quasi-symmetric 2-(49,9,6) design is constructed. This is established by finding a new extremal self-dual [50,25,10] code as a neighbor of one of the four extremal codes discovered by Huffman and Tonchev. A number of new extremal self-dual [50,25,10] codes with other weight enumerators are also found.

AB - Abstract: Huffman and Tonchev discovered four non-isomorphic quasi-symmetric 2-(49,9,6) designs. They arise from extremal self-dual [50,25,10] codes with a certain weight enumerator. In this note, a new quasi-symmetric 2-(49,9,6) design is constructed. This is established by finding a new extremal self-dual [50,25,10] code as a neighbor of one of the four extremal codes discovered by Huffman and Tonchev. A number of new extremal self-dual [50,25,10] codes with other weight enumerators are also found.

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KW - Neighbor

KW - Quasi-symmetric design

KW - Weight enumerator

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A quasi-symmetric 2-(49,9,6) design

Abstract

Keywords

ASJC Scopus subject areas

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