Self-orthogonal codes from symmetric designs with fixed-point-free automorphisms

Masaaki Harada; Vladimir D. Tonchev

doi:10.1016/S0012-365X(02)00553-8

Self-orthogonal codes from symmetric designs with fixed-point-free automorphisms

Masaaki Harada, Vladimir D. Tonchev

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

18 Citations (Scopus)

Abstract

In this paper, we consider a method for constructing non-binary self-orthogonal codes from symmetric designs with fixed-point-free automorphisms. All codes over GF(3) and GF(7) derived from symmetric 2-(v,k,λ) designs with fixed-point-free automorphisms of order p for the parameters (v,k,λ,p)=(27,14,7,3),(40,27,18,5) and (45,12,3,5) are classified. A ternary [63,20,21] code with a record breaking minimum weight is constructed from the symmetric 2-(189,48,12) design found recently by Janko. Several codes over GF(5) and GF(7) that are either optimal or have the largest known minimum weight are constructed from designs obtained from known difference sets.

Original language	English
Pages (from-to)	81-90
Number of pages	10
Journal	Discrete Mathematics
Volume	264
Issue number	1-3
DOIs	https://doi.org/10.1016/S0012-365X(02)00553-8
Publication status	Published - 2003 Mar 6
Externally published	Yes

Keywords

Optimal codes
Self-orthogonal codes
Symmetric designs

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/S0012-365X(02)00553-8

Cite this

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title = "Self-orthogonal codes from symmetric designs with fixed-point-free automorphisms",

abstract = "In this paper, we consider a method for constructing non-binary self-orthogonal codes from symmetric designs with fixed-point-free automorphisms. All codes over GF(3) and GF(7) derived from symmetric 2-(v,k,λ) designs with fixed-point-free automorphisms of order p for the parameters (v,k,λ,p)=(27,14,7,3),(40,27,18,5) and (45,12,3,5) are classified. A ternary [63,20,21] code with a record breaking minimum weight is constructed from the symmetric 2-(189,48,12) design found recently by Janko. Several codes over GF(5) and GF(7) that are either optimal or have the largest known minimum weight are constructed from designs obtained from known difference sets.",

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AU - Harada, Masaaki

AU - Tonchev, Vladimir D.

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N2 - In this paper, we consider a method for constructing non-binary self-orthogonal codes from symmetric designs with fixed-point-free automorphisms. All codes over GF(3) and GF(7) derived from symmetric 2-(v,k,λ) designs with fixed-point-free automorphisms of order p for the parameters (v,k,λ,p)=(27,14,7,3),(40,27,18,5) and (45,12,3,5) are classified. A ternary [63,20,21] code with a record breaking minimum weight is constructed from the symmetric 2-(189,48,12) design found recently by Janko. Several codes over GF(5) and GF(7) that are either optimal or have the largest known minimum weight are constructed from designs obtained from known difference sets.

AB - In this paper, we consider a method for constructing non-binary self-orthogonal codes from symmetric designs with fixed-point-free automorphisms. All codes over GF(3) and GF(7) derived from symmetric 2-(v,k,λ) designs with fixed-point-free automorphisms of order p for the parameters (v,k,λ,p)=(27,14,7,3),(40,27,18,5) and (45,12,3,5) are classified. A ternary [63,20,21] code with a record breaking minimum weight is constructed from the symmetric 2-(189,48,12) design found recently by Janko. Several codes over GF(5) and GF(7) that are either optimal or have the largest known minimum weight are constructed from designs obtained from known difference sets.

KW - Optimal codes

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KW - Symmetric designs

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Self-orthogonal codes from symmetric designs with fixed-point-free automorphisms

Abstract

Keywords

ASJC Scopus subject areas

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