LCD codes and self-orthogonal codes in generalized dihedral group algebras
Abstract Let $$\mathbb {F}_q$$ be a finite field with q elements, $$D_{2n,\,r}$$ a generalized dihedral group with $$\gcd (2n,q)=1$$, and $$\mathbb {F}_q[D_{2n,\,r}]$$ a generalized dihedral group algebra. Firstly, an explicit expression for primitive idempotents of $$\mathbb {F}_q[D_{2n,\,r}]$$ is...
Ausführliche Beschreibung
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| Autor*in: |
Gao, Yanyan [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, LLC, part of Springer Nature 2020 |
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| Übergeordnetes Werk: |
Enthalten in: Designs, codes and cryptography - Springer US, 1991, 88(2020), 11 vom: 02. Juli, Seite 2275-2287 |
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| Übergeordnetes Werk: |
volume:88 ; year:2020 ; number:11 ; day:02 ; month:07 ; pages:2275-2287 |
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| DOI / URN: |
10.1007/s10623-020-00778-z |
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| 520 | |a Abstract Let $$\mathbb {F}_q$$ be a finite field with q elements, $$D_{2n,\,r}$$ a generalized dihedral group with $$\gcd (2n,q)=1$$, and $$\mathbb {F}_q[D_{2n,\,r}]$$ a generalized dihedral group algebra. Firstly, an explicit expression for primitive idempotents of $$\mathbb {F}_q[D_{2n,\,r}]$$ is determined, which extends the results of Brochero Martínez (Finite Fields Appl 35:204–214, 2015). Secondly, all linear complementary dual (LCD) codes and self-orthogonal codes in $$\mathbb {F}_q[D_{2n,\,r}]$$ are precisely described and counted. Some numerical examples are also presented to illustrate our main results. | ||
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10.1007/s10623-020-00778-z doi (DE-627)OLC2120130507 (DE-He213)s10623-020-00778-z-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Gao, Yanyan verfasserin aut LCD codes and self-orthogonal codes in generalized dihedral group algebras 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract Let $$\mathbb {F}_q$$ be a finite field with q elements, $$D_{2n,\,r}$$ a generalized dihedral group with $$\gcd (2n,q)=1$$, and $$\mathbb {F}_q[D_{2n,\,r}]$$ a generalized dihedral group algebra. Firstly, an explicit expression for primitive idempotents of $$\mathbb {F}_q[D_{2n,\,r}]$$ is determined, which extends the results of Brochero Martínez (Finite Fields Appl 35:204–214, 2015). Secondly, all linear complementary dual (LCD) codes and self-orthogonal codes in $$\mathbb {F}_q[D_{2n,\,r}]$$ are precisely described and counted. Some numerical examples are also presented to illustrate our main results. Group algebra Generalized dihedral group LCD codes Self-orthogonal codes Yue, Qin (orcid)0000-0002-2873-5549 aut Wu, Yansheng aut Enthalten in Designs, codes and cryptography Springer US, 1991 88(2020), 11 vom: 02. Juli, Seite 2275-2287 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:88 year:2020 number:11 day:02 month:07 pages:2275-2287 https://doi.org/10.1007/s10623-020-00778-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 88 2020 11 02 07 2275-2287 |
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10.1007/s10623-020-00778-z doi (DE-627)OLC2120130507 (DE-He213)s10623-020-00778-z-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Gao, Yanyan verfasserin aut LCD codes and self-orthogonal codes in generalized dihedral group algebras 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract Let $$\mathbb {F}_q$$ be a finite field with q elements, $$D_{2n,\,r}$$ a generalized dihedral group with $$\gcd (2n,q)=1$$, and $$\mathbb {F}_q[D_{2n,\,r}]$$ a generalized dihedral group algebra. Firstly, an explicit expression for primitive idempotents of $$\mathbb {F}_q[D_{2n,\,r}]$$ is determined, which extends the results of Brochero Martínez (Finite Fields Appl 35:204–214, 2015). Secondly, all linear complementary dual (LCD) codes and self-orthogonal codes in $$\mathbb {F}_q[D_{2n,\,r}]$$ are precisely described and counted. Some numerical examples are also presented to illustrate our main results. Group algebra Generalized dihedral group LCD codes Self-orthogonal codes Yue, Qin (orcid)0000-0002-2873-5549 aut Wu, Yansheng aut Enthalten in Designs, codes and cryptography Springer US, 1991 88(2020), 11 vom: 02. Juli, Seite 2275-2287 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:88 year:2020 number:11 day:02 month:07 pages:2275-2287 https://doi.org/10.1007/s10623-020-00778-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 88 2020 11 02 07 2275-2287 |
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10.1007/s10623-020-00778-z doi (DE-627)OLC2120130507 (DE-He213)s10623-020-00778-z-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Gao, Yanyan verfasserin aut LCD codes and self-orthogonal codes in generalized dihedral group algebras 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract Let $$\mathbb {F}_q$$ be a finite field with q elements, $$D_{2n,\,r}$$ a generalized dihedral group with $$\gcd (2n,q)=1$$, and $$\mathbb {F}_q[D_{2n,\,r}]$$ a generalized dihedral group algebra. Firstly, an explicit expression for primitive idempotents of $$\mathbb {F}_q[D_{2n,\,r}]$$ is determined, which extends the results of Brochero Martínez (Finite Fields Appl 35:204–214, 2015). Secondly, all linear complementary dual (LCD) codes and self-orthogonal codes in $$\mathbb {F}_q[D_{2n,\,r}]$$ are precisely described and counted. Some numerical examples are also presented to illustrate our main results. Group algebra Generalized dihedral group LCD codes Self-orthogonal codes Yue, Qin (orcid)0000-0002-2873-5549 aut Wu, Yansheng aut Enthalten in Designs, codes and cryptography Springer US, 1991 88(2020), 11 vom: 02. Juli, Seite 2275-2287 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:88 year:2020 number:11 day:02 month:07 pages:2275-2287 https://doi.org/10.1007/s10623-020-00778-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 88 2020 11 02 07 2275-2287 |
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10.1007/s10623-020-00778-z doi (DE-627)OLC2120130507 (DE-He213)s10623-020-00778-z-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Gao, Yanyan verfasserin aut LCD codes and self-orthogonal codes in generalized dihedral group algebras 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract Let $$\mathbb {F}_q$$ be a finite field with q elements, $$D_{2n,\,r}$$ a generalized dihedral group with $$\gcd (2n,q)=1$$, and $$\mathbb {F}_q[D_{2n,\,r}]$$ a generalized dihedral group algebra. Firstly, an explicit expression for primitive idempotents of $$\mathbb {F}_q[D_{2n,\,r}]$$ is determined, which extends the results of Brochero Martínez (Finite Fields Appl 35:204–214, 2015). Secondly, all linear complementary dual (LCD) codes and self-orthogonal codes in $$\mathbb {F}_q[D_{2n,\,r}]$$ are precisely described and counted. Some numerical examples are also presented to illustrate our main results. Group algebra Generalized dihedral group LCD codes Self-orthogonal codes Yue, Qin (orcid)0000-0002-2873-5549 aut Wu, Yansheng aut Enthalten in Designs, codes and cryptography Springer US, 1991 88(2020), 11 vom: 02. Juli, Seite 2275-2287 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:88 year:2020 number:11 day:02 month:07 pages:2275-2287 https://doi.org/10.1007/s10623-020-00778-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 88 2020 11 02 07 2275-2287 |
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10.1007/s10623-020-00778-z doi (DE-627)OLC2120130507 (DE-He213)s10623-020-00778-z-p DE-627 ger DE-627 rakwb eng 004 VZ 17,1 ssgn Gao, Yanyan verfasserin aut LCD codes and self-orthogonal codes in generalized dihedral group algebras 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract Let $$\mathbb {F}_q$$ be a finite field with q elements, $$D_{2n,\,r}$$ a generalized dihedral group with $$\gcd (2n,q)=1$$, and $$\mathbb {F}_q[D_{2n,\,r}]$$ a generalized dihedral group algebra. Firstly, an explicit expression for primitive idempotents of $$\mathbb {F}_q[D_{2n,\,r}]$$ is determined, which extends the results of Brochero Martínez (Finite Fields Appl 35:204–214, 2015). Secondly, all linear complementary dual (LCD) codes and self-orthogonal codes in $$\mathbb {F}_q[D_{2n,\,r}]$$ are precisely described and counted. Some numerical examples are also presented to illustrate our main results. Group algebra Generalized dihedral group LCD codes Self-orthogonal codes Yue, Qin (orcid)0000-0002-2873-5549 aut Wu, Yansheng aut Enthalten in Designs, codes and cryptography Springer US, 1991 88(2020), 11 vom: 02. Juli, Seite 2275-2287 (DE-627)130994197 (DE-600)1082042-5 (DE-576)029154375 0925-1022 nnns volume:88 year:2020 number:11 day:02 month:07 pages:2275-2287 https://doi.org/10.1007/s10623-020-00778-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 88 2020 11 02 07 2275-2287 |
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Abstract Let $$\mathbb {F}_q$$ be a finite field with q elements, $$D_{2n,\,r}$$ a generalized dihedral group with $$\gcd (2n,q)=1$$, and $$\mathbb {F}_q[D_{2n,\,r}]$$ a generalized dihedral group algebra. Firstly, an explicit expression for primitive idempotents of $$\mathbb {F}_q[D_{2n,\,r}]$$ is determined, which extends the results of Brochero Martínez (Finite Fields Appl 35:204–214, 2015). Secondly, all linear complementary dual (LCD) codes and self-orthogonal codes in $$\mathbb {F}_q[D_{2n,\,r}]$$ are precisely described and counted. Some numerical examples are also presented to illustrate our main results. © Springer Science+Business Media, LLC, part of Springer Nature 2020 |
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Abstract Let $$\mathbb {F}_q$$ be a finite field with q elements, $$D_{2n,\,r}$$ a generalized dihedral group with $$\gcd (2n,q)=1$$, and $$\mathbb {F}_q[D_{2n,\,r}]$$ a generalized dihedral group algebra. Firstly, an explicit expression for primitive idempotents of $$\mathbb {F}_q[D_{2n,\,r}]$$ is determined, which extends the results of Brochero Martínez (Finite Fields Appl 35:204–214, 2015). Secondly, all linear complementary dual (LCD) codes and self-orthogonal codes in $$\mathbb {F}_q[D_{2n,\,r}]$$ are precisely described and counted. Some numerical examples are also presented to illustrate our main results. © Springer Science+Business Media, LLC, part of Springer Nature 2020 |
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Abstract Let $$\mathbb {F}_q$$ be a finite field with q elements, $$D_{2n,\,r}$$ a generalized dihedral group with $$\gcd (2n,q)=1$$, and $$\mathbb {F}_q[D_{2n,\,r}]$$ a generalized dihedral group algebra. Firstly, an explicit expression for primitive idempotents of $$\mathbb {F}_q[D_{2n,\,r}]$$ is determined, which extends the results of Brochero Martínez (Finite Fields Appl 35:204–214, 2015). Secondly, all linear complementary dual (LCD) codes and self-orthogonal codes in $$\mathbb {F}_q[D_{2n,\,r}]$$ are precisely described and counted. Some numerical examples are also presented to illustrate our main results. © Springer Science+Business Media, LLC, part of Springer Nature 2020 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2120130507</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230504174234.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230504s2020 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10623-020-00778-z</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2120130507</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10623-020-00778-z-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">004</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Gao, Yanyan</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">LCD codes and self-orthogonal codes in generalized dihedral group algebras</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2020</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media, LLC, part of Springer Nature 2020</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Let $$\mathbb {F}_q$$ be a finite field with q elements, $$D_{2n,\,r}$$ a generalized dihedral group with $$\gcd (2n,q)=1$$, and $$\mathbb {F}_q[D_{2n,\,r}]$$ a generalized dihedral group algebra. Firstly, an explicit expression for primitive idempotents of $$\mathbb {F}_q[D_{2n,\,r}]$$ is determined, which extends the results of Brochero Martínez (Finite Fields Appl 35:204–214, 2015). Secondly, all linear complementary dual (LCD) codes and self-orthogonal codes in $$\mathbb {F}_q[D_{2n,\,r}]$$ are precisely described and counted. Some numerical examples are also presented to illustrate our main results.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Group algebra</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Generalized dihedral group</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">LCD codes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Self-orthogonal codes</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Yue, Qin</subfield><subfield code="0">(orcid)0000-0002-2873-5549</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wu, Yansheng</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Designs, codes and cryptography</subfield><subfield code="d">Springer US, 1991</subfield><subfield code="g">88(2020), 11 vom: 02. 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