Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2018, Cilt: 5 Sayı: 1, 45 - 49, 15.01.2018
https://doi.org/10.13069/jacodesmath.369864

Öz

Kaynakça

  • [1] J. Chifman, Note on direct products of certain classes of finite groups, Commun. Algebra 37(5) (2009) 1831–1842.
  • [2] R. Dedekind, Ueber Gruppen, deren sämmtliche Theiler Normaltheiler sind, Math. Ann. 48(4) (1897) 548–561.
  • [3] S. Dougherty, J.-L. Kim, P. Solé, Open problems in coding theory, Contemp. Math. 634 (2015) 79–99.
  • [4] K. Iwasawa, Über die endlichen Gruppen und die Verbände ihrer Untergruppen, J. Fac. Sci. Imp. Univ. Tokyo. Sect. I. 4 (1941) 171–199.
  • [5] R. Schmidt, Subgroup Lattices of Groups, Walter de Gruyter, Berlin, 1994.
  • [6] M. Suzuki, On the lattice of subgroups of finite groups, Trans. Amer. Math. Soc. 70(2) (1951) 345–371.
  • [7] G. Zacher, Caratterizzazione dei gruppi immagini omomorfe duali di un gruppo finito, Rend. Sem. Mat. Univ. Padova 31 (1961) 412–422.

No MacWilliams duality for codes over nonabelian groups

Yıl 2018, Cilt: 5 Sayı: 1, 45 - 49, 15.01.2018
https://doi.org/10.13069/jacodesmath.369864

Öz

Dougherty, Kim, and Sol\'e [3] have asked whether there is a duality theory and a MacWilliams formula for codes over nonabelian groups, or more generally, whether there is any subclass of nonabelian groups which have such a duality theory. We answer this in the negative by showing that there does not exist a nonabelian group $G$ with a duality theory on the subgroups of $G^n$ for all $n$.

Kaynakça

  • [1] J. Chifman, Note on direct products of certain classes of finite groups, Commun. Algebra 37(5) (2009) 1831–1842.
  • [2] R. Dedekind, Ueber Gruppen, deren sämmtliche Theiler Normaltheiler sind, Math. Ann. 48(4) (1897) 548–561.
  • [3] S. Dougherty, J.-L. Kim, P. Solé, Open problems in coding theory, Contemp. Math. 634 (2015) 79–99.
  • [4] K. Iwasawa, Über die endlichen Gruppen und die Verbände ihrer Untergruppen, J. Fac. Sci. Imp. Univ. Tokyo. Sect. I. 4 (1941) 171–199.
  • [5] R. Schmidt, Subgroup Lattices of Groups, Walter de Gruyter, Berlin, 1994.
  • [6] M. Suzuki, On the lattice of subgroups of finite groups, Trans. Amer. Math. Soc. 70(2) (1951) 345–371.
  • [7] G. Zacher, Caratterizzazione dei gruppi immagini omomorfe duali di un gruppo finito, Rend. Sem. Mat. Univ. Padova 31 (1961) 412–422.
Toplam 7 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Makaleler
Yazarlar

M. Ryan Julian Jr. Bu kişi benim 0000-0002-6117-1415

Yayımlanma Tarihi 15 Ocak 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 5 Sayı: 1

Kaynak Göster

APA Julian Jr., M. R. (2018). No MacWilliams duality for codes over nonabelian groups. Journal of Algebra Combinatorics Discrete Structures and Applications, 5(1), 45-49. https://doi.org/10.13069/jacodesmath.369864
AMA Julian Jr. MR. No MacWilliams duality for codes over nonabelian groups. Journal of Algebra Combinatorics Discrete Structures and Applications. Ocak 2018;5(1):45-49. doi:10.13069/jacodesmath.369864
Chicago Julian Jr., M. Ryan. “No MacWilliams Duality for Codes over Nonabelian Groups”. Journal of Algebra Combinatorics Discrete Structures and Applications 5, sy. 1 (Ocak 2018): 45-49. https://doi.org/10.13069/jacodesmath.369864.
EndNote Julian Jr. MR (01 Ocak 2018) No MacWilliams duality for codes over nonabelian groups. Journal of Algebra Combinatorics Discrete Structures and Applications 5 1 45–49.
IEEE M. R. Julian Jr., “No MacWilliams duality for codes over nonabelian groups”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 5, sy. 1, ss. 45–49, 2018, doi: 10.13069/jacodesmath.369864.
ISNAD Julian Jr., M. Ryan. “No MacWilliams Duality for Codes over Nonabelian Groups”. Journal of Algebra Combinatorics Discrete Structures and Applications 5/1 (Ocak 2018), 45-49. https://doi.org/10.13069/jacodesmath.369864.
JAMA Julian Jr. MR. No MacWilliams duality for codes over nonabelian groups. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018;5:45–49.
MLA Julian Jr., M. Ryan. “No MacWilliams Duality for Codes over Nonabelian Groups”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 5, sy. 1, 2018, ss. 45-49, doi:10.13069/jacodesmath.369864.
Vancouver Julian Jr. MR. No MacWilliams duality for codes over nonabelian groups. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018;5(1):45-9.