Flaviana S. Dutra, Raul A. Ferraz, C. Polcino Milies, “Semisimple group codes and dihedral codes”, Algebra Discrete Math., 2009, no. 3, 28

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Algebra and Discrete Mathematics, 2009, Issue 3, Pages 28–48 (Mi adm131)

This article is cited in 15 scientific papers (total in 15 papers)

RESEARCH ARTICLE

Semisimple group codes and dihedral codes

Flaviana S. Dutra^a, Raul A. Ferraz^b, C. Polcino Milies^b

^a Departamento de Matemática e Estatística (DME), Pontifícia Universidade Católica de Minas Gerais, Av. Dom José Gaspar, 500, Cep 30.535–901,Belo Horizonte, MG, Brazil
^b Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, Cep 05311–970, São Paulo, SP, Brazil

Full-text PDF (304 kB) Citations (15)

Abstract: We consider codes that are given as two-sided ideals in a semisimple finite group algebra

${\mathbb F}_qG$ defined by idempotents constructed from subgroups of

$G$ in a natural way and compute their dimensions and weights. We give a criterion to decide when these ideals are all the minimal two-sided ideals of

${\mathbb F}_qG$ in the case when

$G$ is a dihedral group and extend these results also to a family of quaternion group codes. In the final section, we give a method of decoding; i.e., of finding and correcting eventual transmission errors.

Keywords: group code, minimal code, group algebra, idempotent, dihedral group, quaternion group.

Received: 20.08.2009
Revised: 24.09.2009

Bibliographic databases:

Document Type: Article

MSC: 94B15, 94B60, 16S34, 20C05

Language: English

Citation: Flaviana S. Dutra, Raul A. Ferraz, C. Polcino Milies, “Semisimple group codes and dihedral codes”, Algebra Discrete Math., 2009, no. 3, 28–48

Citation in format AMSBIB

\Bibitem{DutFerMil09}

\by Flaviana~S.~Dutra, Raul~A.~Ferraz, C.~Polcino~Milies

\paper Semisimple group codes and dihedral codes

\jour Algebra Discrete Math.

\yr 2009

\issue 3

\pages 28--48

\mathnet{http://mi.mathnet.ru/adm131}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2640386}

\zmath{https://zbmath.org/?q=an:1199.94110}

Linking options:

https://www.mathnet.ru/eng/adm131

https://www.mathnet.ru/eng/adm/y2009/i3/p28

This publication is cited in the following 15 articles:

Ferraz R.A., Milies C.P., “Essential Idempotents in Group Algebras and Coding Theory”, Indian J. Pure Appl. Math., 52:3 (2021), 747–760
Ferraz R.A., Milies C.P., Taufer E., “Left Ideals of Matrix Rings and Error-Correcting Codes”, Appl. Algebr. Eng. Commun. Comput., 32:3, SI (2021), 311–320
Creedon L., Hughes K., Szabo S., “A Comparison of Group Algebras of Dihedral and Quaternion Groups”, Appl. Algebr. Eng. Commun. Comput., 32:3, SI (2021), 245–264
Cao Yu., Cao Y., Fu F.-W., Gao J., “Self-Dual Binary [8M, 4M]-Codes Constructed By Left Ideals of the Dihedral Group Algebra F-2[D-8M]”, IEEE Trans. Inf. Theory, 66:6 (2020), 3555–3571
Li F., Yue Q., Wu Ya., “Lcd and Self-Orthogonal Group Codes in a Finite Abelian P-Group Algebra”, IEEE Trans. Inf. Theory, 66:5 (2020), 2717–2728
Dougherty S.T., Fernandez-Cordoba C., Ten-Valls R., Yildiz B., “Quaternary Group Ring Codes: Ranks, Kernels and Self-Dual Codes”, Adv. Math. Commun., 14:2 (2020), 319–332
Assuena S., Milies C.P., “Good Codes From Metacyclic Groups”, Rings, Modules and Codes, Contemporary Mathematics, 727, eds. Leroy A., Lomp C., LopezPermouth S., Oggier F., Amer Mathematical Soc, 2019, 39–47
Sehrawat S., Pruthi M., “Codes Over Non-Abelian Groups”, J. Inform. Optim. Science, 40:3 (2019), 789–804
Abdallaoui M.A., El Badry M., Haily A., “Idempotents and Codes in Some Non Semi-Simple Metacyclic Group Algebras”, Finite Fields their Appl., 51 (2018), 62–70
Sehrawat S., Pruthi M., “Codes Over Dihedral Groups”, J. Inform. Optim. Science, 39:4 (2018), 889–901
Cao Yu., Cao Y., Gao J., “A Class of Left Dihedral Codes Over Rings F-Q + Uf(Q)”, IEICE Trans. Fundam. Electron. Commun. Comput. Sci., E100A:12 (2017), 2585–2593
Huang H., Li Yu., Tang G., “on -Clean Non-Commutative Group Rings”, J. Algebra. Appl., 15:8 (2016), 1650150
Cao Y., Cao Yu., Fu F.-W., “Concatenated Structure of Left Dihedral Codes”, Finite Fields their Appl., 38 (2016), 93–115
Cao Yu., Cao Y., Fu F.-W., “on Left Quaternion Codes”, Int. J. Comput. Math., 93:10 (2016), 1629–1649
Martinez F.E.B., “Structure of Finite Dihedral Group Algebra”, Finite Fields their Appl., 35 (2015), 204–214

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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