Araştırma Makalesi

The extension problem for Lee and Euclidean weights

Cilt: 4 Sayı: 2 (Special Issue: Noncommutative rings and their applications) 10 Ocak 2017
  • Philippe Langevin
  • Jay A. Wood
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The extension problem for Lee and Euclidean weights

Öz

The extension problem is solved for the Lee and Euclidean weights over three families of rings of the form $\Z/N\Z$: $N=2^{\ell + 1}$, $N=3^{\ell + 1}$, or $N=p=2q+1$ with $p$ and $q$ prime. The extension problem is solved for the Euclidean PSK weight over $\Z/N\Z$ for all $N$.

Anahtar Kelimeler

Kaynakça

  1. [1] A. Barra, Equivalence Theorems and the Local-Global Property, ProQuest LLC, PhD thesis University of Kentucky, Ann Arbor, MI, USA, 2012.
  2. [2] A. Barra, H. Gluesing–Luerssen, MacWilliams extension theorems and the local–global property for codes over Frobenius rings, J. Pure Appl. Algebra 219(4) (2015) 703–728.
  3. [3] S. Dyshko, P. Langevin, J. A. Wood, Deux analogues au déterminant de Maillet, C. R. Math. Acad. Sci. Paris 354(7) (2016) 649–652.
  4. [4] F. G. Frobenius, Gesammelte Abhandlungen, Springer–Verlag, Berlin, 1968.
  5. [5] M. Greferath, T. Honold, C. Mc Fadden, J. A.Wood, J. Zumbrägel, MacWilliams’ extension theorem for bi-invariant weights over finite principal ideal rings, J. Combin. Theory Ser. A 125 (2014) 177–193.
  6. [6] M. Greferath, C. Mc Fadden, J. Zumbrägel, Characteristics of invariant weights related to code equivalence over rings, Des. Codes Cryptogr. 66(1) (2013) 145–156.
  7. [7] M. Greferath, S. E. Schmidt, Finite–ring combinatorics and MacWilliams’ equivalence theorem, J. Combin. Theory Ser. A 92(1) (2000) 17–28.
  8. [8] W. Heise, T. Honold, Homogeneous and egalitarian weights on finite rings, Proceedings of the Seventh International Workshop on Algebraic and Combinatorial Coding Theory (ACCT-2000), Bansko, Bulgaria, 183–188, 2000.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Mühendislik

Bölüm

Araştırma Makalesi

Yazarlar

Philippe Langevin Bu kişi benim

Jay A. Wood Bu kişi benim

Yayımlanma Tarihi

10 Ocak 2017

Gönderilme Tarihi

12 Haziran 2015

Kabul Tarihi

-

Yayımlandığı Sayı

Yıl 2017 Cilt: 4 Sayı: 2 (Special Issue: Noncommutative rings and their applications)

Kaynak Göster

APA
Langevin, P., & Wood, J. A. (2017). The extension problem for Lee and Euclidean weights. Journal of Algebra Combinatorics Discrete Structures and Applications, 4(2 (Special Issue: Noncommutative rings and their applications), 207-217. https://doi.org/10.13069/jacodesmath.284970
AMA
1.Langevin P, Wood JA. The extension problem for Lee and Euclidean weights. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017;4(2 (Special Issue: Noncommutative rings and their applications):207-217. doi:10.13069/jacodesmath.284970
Chicago
Langevin, Philippe, ve Jay A. Wood. 2017. “The extension problem for Lee and Euclidean weights”. Journal of Algebra Combinatorics Discrete Structures and Applications 4 (2 (Special Issue: Noncommutative rings and their applications): 207-17. https://doi.org/10.13069/jacodesmath.284970.
EndNote
Langevin P, Wood JA (01 Mayıs 2017) The extension problem for Lee and Euclidean weights. Journal of Algebra Combinatorics Discrete Structures and Applications 4 2 (Special Issue: Noncommutative rings and their applications) 207–217.
IEEE
[1]P. Langevin ve J. A. Wood, “The extension problem for Lee and Euclidean weights”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 4, sy 2 (Special Issue: Noncommutative rings and their applications), ss. 207–217, May. 2017, doi: 10.13069/jacodesmath.284970.
ISNAD
Langevin, Philippe - Wood, Jay A. “The extension problem for Lee and Euclidean weights”. Journal of Algebra Combinatorics Discrete Structures and Applications 4/2 (Special Issue: Noncommutative rings and their applications) (01 Mayıs 2017): 207-217. https://doi.org/10.13069/jacodesmath.284970.
JAMA
1.Langevin P, Wood JA. The extension problem for Lee and Euclidean weights. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017;4:207–217.
MLA
Langevin, Philippe, ve Jay A. Wood. “The extension problem for Lee and Euclidean weights”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 4, sy 2 (Special Issue: Noncommutative rings and their applications), Mayıs 2017, ss. 207-1, doi:10.13069/jacodesmath.284970.
Vancouver
1.Philippe Langevin, Jay A. Wood. The extension problem for Lee and Euclidean weights. Journal of Algebra Combinatorics Discrete Structures and Applications. 01 Mayıs 2017;4(2 (Special Issue: Noncommutative rings and their applications):207-1. doi:10.13069/jacodesmath.284970

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