On the automorphism group of a binary self-dual $$[120, 60, 24]$$ code
Abstract We prove that an automorphism of order 3 of a putative binary self-dual $$[120, 60, 24]$$ code $$C$$ has no fixed points. Moreover, the order of the automorphism group of $$C$$ divides $$2^a\cdot 3 \cdot 5\cdot 7\cdot 19\cdot 23\cdot 29$$ with $$a\in \mathbb N _0$$. Automorphisms of odd com...
Ausführliche Beschreibung
Gespeichert in:
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Bouyuklieva, Stefka [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Applicable algebra in engineering, communication and computing - Springer Berlin Heidelberg, 1990, 24(2013), 3-4 vom: 26. Juni, Seite 201-214 |
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| Übergeordnetes Werk: |
volume:24 ; year:2013 ; number:3-4 ; day:26 ; month:06 ; pages:201-214 |
| Links: |
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| DOI / URN: |
10.1007/s00200-013-0193-0 |
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OLC2075499071 |
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| 520 | |a Abstract We prove that an automorphism of order 3 of a putative binary self-dual $$[120, 60, 24]$$ code $$C$$ has no fixed points. Moreover, the order of the automorphism group of $$C$$ divides $$2^a\cdot 3 \cdot 5\cdot 7\cdot 19\cdot 23\cdot 29$$ with $$a\in \mathbb N _0$$. Automorphisms of odd composite order $$r$$ may occur only for $$r=15, 57$$ or $$r=115$$ with corresponding cycle structures $$3 \cdot 5$$-$$(0,0,8;0), 3\cdot 19$$-$$(2,0,2;0)$$ or $$5 \cdot 23$$-$$(1,0,1;0)$$ respectively. In case that all involutions act fixed point freely we have $$|\mathrm{Aut}(C)| \le 920$$, and $$\mathrm{Aut}(C)$$ is solvable if it contains an element of prime order $$p \ge 7$$. Moreover, the alternating group $$\mathrm{A}_5$$ is the only non-abelian composition factor which may occur in $$\mathrm{Aut}(C)$$. | ||
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10.1007/s00200-013-0193-0 doi (DE-627)OLC2075499071 (DE-He213)s00200-013-0193-0-p DE-627 ger DE-627 rakwb eng 510 620 004 VZ 510 004 600 VZ 11 ssgn Bouyuklieva, Stefka verfasserin aut On the automorphism group of a binary self-dual $$[120, 60, 24]$$ code 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract We prove that an automorphism of order 3 of a putative binary self-dual $$[120, 60, 24]$$ code $$C$$ has no fixed points. Moreover, the order of the automorphism group of $$C$$ divides $$2^a\cdot 3 \cdot 5\cdot 7\cdot 19\cdot 23\cdot 29$$ with $$a\in \mathbb N _0$$. Automorphisms of odd composite order $$r$$ may occur only for $$r=15, 57$$ or $$r=115$$ with corresponding cycle structures $$3 \cdot 5$$-$$(0,0,8;0), 3\cdot 19$$-$$(2,0,2;0)$$ or $$5 \cdot 23$$-$$(1,0,1;0)$$ respectively. In case that all involutions act fixed point freely we have $$|\mathrm{Aut}(C)| \le 920$$, and $$\mathrm{Aut}(C)$$ is solvable if it contains an element of prime order $$p \ge 7$$. Moreover, the alternating group $$\mathrm{A}_5$$ is the only non-abelian composition factor which may occur in $$\mathrm{Aut}(C)$$. Self-dual codes Automorphisms Extremal codes de la Cruz, Javier aut Willems, Wolfgang aut Enthalten in Applicable algebra in engineering, communication and computing Springer Berlin Heidelberg, 1990 24(2013), 3-4 vom: 26. Juni, Seite 201-214 (DE-627)130915807 (DE-600)1051032-1 (DE-576)025004964 0938-1279 nnns volume:24 year:2013 number:3-4 day:26 month:06 pages:201-214 https://doi.org/10.1007/s00200-013-0193-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4126 GBV_ILN_4247 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4318 AR 24 2013 3-4 26 06 201-214 |
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10.1007/s00200-013-0193-0 doi (DE-627)OLC2075499071 (DE-He213)s00200-013-0193-0-p DE-627 ger DE-627 rakwb eng 510 620 004 VZ 510 004 600 VZ 11 ssgn Bouyuklieva, Stefka verfasserin aut On the automorphism group of a binary self-dual $$[120, 60, 24]$$ code 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract We prove that an automorphism of order 3 of a putative binary self-dual $$[120, 60, 24]$$ code $$C$$ has no fixed points. Moreover, the order of the automorphism group of $$C$$ divides $$2^a\cdot 3 \cdot 5\cdot 7\cdot 19\cdot 23\cdot 29$$ with $$a\in \mathbb N _0$$. Automorphisms of odd composite order $$r$$ may occur only for $$r=15, 57$$ or $$r=115$$ with corresponding cycle structures $$3 \cdot 5$$-$$(0,0,8;0), 3\cdot 19$$-$$(2,0,2;0)$$ or $$5 \cdot 23$$-$$(1,0,1;0)$$ respectively. In case that all involutions act fixed point freely we have $$|\mathrm{Aut}(C)| \le 920$$, and $$\mathrm{Aut}(C)$$ is solvable if it contains an element of prime order $$p \ge 7$$. Moreover, the alternating group $$\mathrm{A}_5$$ is the only non-abelian composition factor which may occur in $$\mathrm{Aut}(C)$$. Self-dual codes Automorphisms Extremal codes de la Cruz, Javier aut Willems, Wolfgang aut Enthalten in Applicable algebra in engineering, communication and computing Springer Berlin Heidelberg, 1990 24(2013), 3-4 vom: 26. Juni, Seite 201-214 (DE-627)130915807 (DE-600)1051032-1 (DE-576)025004964 0938-1279 nnns volume:24 year:2013 number:3-4 day:26 month:06 pages:201-214 https://doi.org/10.1007/s00200-013-0193-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4126 GBV_ILN_4247 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4318 AR 24 2013 3-4 26 06 201-214 |
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10.1007/s00200-013-0193-0 doi (DE-627)OLC2075499071 (DE-He213)s00200-013-0193-0-p DE-627 ger DE-627 rakwb eng 510 620 004 VZ 510 004 600 VZ 11 ssgn Bouyuklieva, Stefka verfasserin aut On the automorphism group of a binary self-dual $$[120, 60, 24]$$ code 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2013 Abstract We prove that an automorphism of order 3 of a putative binary self-dual $$[120, 60, 24]$$ code $$C$$ has no fixed points. Moreover, the order of the automorphism group of $$C$$ divides $$2^a\cdot 3 \cdot 5\cdot 7\cdot 19\cdot 23\cdot 29$$ with $$a\in \mathbb N _0$$. Automorphisms of odd composite order $$r$$ may occur only for $$r=15, 57$$ or $$r=115$$ with corresponding cycle structures $$3 \cdot 5$$-$$(0,0,8;0), 3\cdot 19$$-$$(2,0,2;0)$$ or $$5 \cdot 23$$-$$(1,0,1;0)$$ respectively. In case that all involutions act fixed point freely we have $$|\mathrm{Aut}(C)| \le 920$$, and $$\mathrm{Aut}(C)$$ is solvable if it contains an element of prime order $$p \ge 7$$. Moreover, the alternating group $$\mathrm{A}_5$$ is the only non-abelian composition factor which may occur in $$\mathrm{Aut}(C)$$. Self-dual codes Automorphisms Extremal codes de la Cruz, Javier aut Willems, Wolfgang aut Enthalten in Applicable algebra in engineering, communication and computing Springer Berlin Heidelberg, 1990 24(2013), 3-4 vom: 26. Juni, Seite 201-214 (DE-627)130915807 (DE-600)1051032-1 (DE-576)025004964 0938-1279 nnns volume:24 year:2013 number:3-4 day:26 month:06 pages:201-214 https://doi.org/10.1007/s00200-013-0193-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4126 GBV_ILN_4247 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4318 AR 24 2013 3-4 26 06 201-214 |
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Enthalten in Applicable algebra in engineering, communication and computing 24(2013), 3-4 vom: 26. Juni, Seite 201-214 volume:24 year:2013 number:3-4 day:26 month:06 pages:201-214 |
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510 620 004 VZ 510 004 600 VZ 11 ssgn On the automorphism group of a binary self-dual $$[120, 60, 24]$$ code Self-dual codes Automorphisms Extremal codes |
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On the automorphism group of a binary self-dual $$[120, 60, 24]$$ code |
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On the automorphism group of a binary self-dual $$[120, 60, 24]$$ code |
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Bouyuklieva, Stefka |
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Applicable algebra in engineering, communication and computing |
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on the automorphism group of a binary self-dual $$[120, 60, 24]$$ code |
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On the automorphism group of a binary self-dual $$[120, 60, 24]$$ code |
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Abstract We prove that an automorphism of order 3 of a putative binary self-dual $$[120, 60, 24]$$ code $$C$$ has no fixed points. Moreover, the order of the automorphism group of $$C$$ divides $$2^a\cdot 3 \cdot 5\cdot 7\cdot 19\cdot 23\cdot 29$$ with $$a\in \mathbb N _0$$. Automorphisms of odd composite order $$r$$ may occur only for $$r=15, 57$$ or $$r=115$$ with corresponding cycle structures $$3 \cdot 5$$-$$(0,0,8;0), 3\cdot 19$$-$$(2,0,2;0)$$ or $$5 \cdot 23$$-$$(1,0,1;0)$$ respectively. In case that all involutions act fixed point freely we have $$|\mathrm{Aut}(C)| \le 920$$, and $$\mathrm{Aut}(C)$$ is solvable if it contains an element of prime order $$p \ge 7$$. Moreover, the alternating group $$\mathrm{A}_5$$ is the only non-abelian composition factor which may occur in $$\mathrm{Aut}(C)$$. © Springer-Verlag Berlin Heidelberg 2013 |
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Abstract We prove that an automorphism of order 3 of a putative binary self-dual $$[120, 60, 24]$$ code $$C$$ has no fixed points. Moreover, the order of the automorphism group of $$C$$ divides $$2^a\cdot 3 \cdot 5\cdot 7\cdot 19\cdot 23\cdot 29$$ with $$a\in \mathbb N _0$$. Automorphisms of odd composite order $$r$$ may occur only for $$r=15, 57$$ or $$r=115$$ with corresponding cycle structures $$3 \cdot 5$$-$$(0,0,8;0), 3\cdot 19$$-$$(2,0,2;0)$$ or $$5 \cdot 23$$-$$(1,0,1;0)$$ respectively. In case that all involutions act fixed point freely we have $$|\mathrm{Aut}(C)| \le 920$$, and $$\mathrm{Aut}(C)$$ is solvable if it contains an element of prime order $$p \ge 7$$. Moreover, the alternating group $$\mathrm{A}_5$$ is the only non-abelian composition factor which may occur in $$\mathrm{Aut}(C)$$. © Springer-Verlag Berlin Heidelberg 2013 |
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Abstract We prove that an automorphism of order 3 of a putative binary self-dual $$[120, 60, 24]$$ code $$C$$ has no fixed points. Moreover, the order of the automorphism group of $$C$$ divides $$2^a\cdot 3 \cdot 5\cdot 7\cdot 19\cdot 23\cdot 29$$ with $$a\in \mathbb N _0$$. Automorphisms of odd composite order $$r$$ may occur only for $$r=15, 57$$ or $$r=115$$ with corresponding cycle structures $$3 \cdot 5$$-$$(0,0,8;0), 3\cdot 19$$-$$(2,0,2;0)$$ or $$5 \cdot 23$$-$$(1,0,1;0)$$ respectively. In case that all involutions act fixed point freely we have $$|\mathrm{Aut}(C)| \le 920$$, and $$\mathrm{Aut}(C)$$ is solvable if it contains an element of prime order $$p \ge 7$$. Moreover, the alternating group $$\mathrm{A}_5$$ is the only non-abelian composition factor which may occur in $$\mathrm{Aut}(C)$$. © Springer-Verlag Berlin Heidelberg 2013 |
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