Extremal self-dual [50, 25, 10] codes with automorphisms of order 3 and quasi-symmetric 2-(49, 9,6) designs

Stefka Bouyuklieva; Masaaki Harada

doi:10.1023/A:1022588407585

Extremal self-dual [50, 25, 10] codes with automorphisms of order 3 and quasi-symmetric 2-(49, 9,6) designs

Stefka Bouyuklieva, Masaaki Harada

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

6 Citations (Scopus)

Abstract

Five non-isomorphic quasi-symmetric 2-(49, 9, 6) designs are known. They arise from extremal self-dual [50, 25, 10] codes with a certain weight enumerator. Four of them have an automorphism of order 3 fixing two points. In this paper, it is shown that there are exactly 48 inequivalent extremal self-dual [50, 25, 10] code with this weight enumerator and an automorphism of order 3 fixing two points. 44 new quasi-symmetric 2-(49, 9, 6) designs with an automorphism of order 3 are constructed from these codes.

Original language	English
Pages (from-to)	163-169
Number of pages	7
Journal	Designs, Codes, and Cryptography
Volume	28
Issue number	2
DOIs	https://doi.org/10.1023/A:1022588407585
Publication status	Published - 2003 Mar
Externally published	Yes

Keywords

automorphisms
quasi-symmetric design
self-dual code

ASJC Scopus subject areas

Computer Science Applications
Applied Mathematics

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10.1023/A:1022588407585

Cite this

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abstract = "Five non-isomorphic quasi-symmetric 2-(49, 9, 6) designs are known. They arise from extremal self-dual [50, 25, 10] codes with a certain weight enumerator. Four of them have an automorphism of order 3 fixing two points. In this paper, it is shown that there are exactly 48 inequivalent extremal self-dual [50, 25, 10] code with this weight enumerator and an automorphism of order 3 fixing two points. 44 new quasi-symmetric 2-(49, 9, 6) designs with an automorphism of order 3 are constructed from these codes.",

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Y1 - 2003/3

N2 - Five non-isomorphic quasi-symmetric 2-(49, 9, 6) designs are known. They arise from extremal self-dual [50, 25, 10] codes with a certain weight enumerator. Four of them have an automorphism of order 3 fixing two points. In this paper, it is shown that there are exactly 48 inequivalent extremal self-dual [50, 25, 10] code with this weight enumerator and an automorphism of order 3 fixing two points. 44 new quasi-symmetric 2-(49, 9, 6) designs with an automorphism of order 3 are constructed from these codes.

AB - Five non-isomorphic quasi-symmetric 2-(49, 9, 6) designs are known. They arise from extremal self-dual [50, 25, 10] codes with a certain weight enumerator. Four of them have an automorphism of order 3 fixing two points. In this paper, it is shown that there are exactly 48 inequivalent extremal self-dual [50, 25, 10] code with this weight enumerator and an automorphism of order 3 fixing two points. 44 new quasi-symmetric 2-(49, 9, 6) designs with an automorphism of order 3 are constructed from these codes.

KW - automorphisms

KW - quasi-symmetric design

KW - self-dual code

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Extremal self-dual [50, 25, 10] codes with automorphisms of order 3 and quasi-symmetric 2-(49, 9,6) designs

Abstract

Keywords

ASJC Scopus subject areas

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