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BibTex RIS Kaynak Göster

Yıl 2019, , 94 - 101, 30.04.2019

Jean Jacques Ferdinand Randriamiarampanahy Harinaivo Andriatahiny Toussaint Joseph Rabeherimanana

https://doi.org/10.36753/mathenot.559263

Öz

Kaynakça

  • [1] Adams, W. and Loustaunau, P., An Introduction to Groebner Bases, American Mathematical Society, Vol.3, 1994.
  • [2] Borges-quintana, M., Borges-Trenard, M., Fitzpatrick P. and Martinez-Moro E., Groebner bases and combinatorics for binary codes, Applicable Algebra in Engineering Communication and Computing - AAECC 19(2008), 393-411.
  • [3] Buchberger, B., An Algorithm for Finding the Basis Elements of the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal, PhD thesis, University of Innsbruck, 1965.
  • [4] Cooper, A., Towards a new method of decoding Algebraic codes using Groebner bases, Transactions 10th Army Conf. Appl. Math. Comp. 93(1992), 293-297.
  • [5] Cox, D., Little J. and O’Shea D., Ideals, Varieties, and Algorithms, Springer, 1996.
  • [6] Cox, D., Little J. and O’Shea D., Using Algebraic Geometry, Springer, 1998.
  • [7] Drton, M., Sturmfels B., Sullivan S., Lectures on Algebraic Statistics, Birkhäuser, Basel, 2009.
  • [8] Dück, N. and Zimmermann, K.H., Gröbner bases for perfect binary linear codes, International Journal of Pure and Applied Mathematics 91(2014), no.2, 155-167.
  • [9] Dück, N. and Zimmermann, K.H., Standard Bases for binary Linear Codes, International Journal of Pure and Applied Mathematics 80(2012), no.3, 315-329.
  • [10] Dück, N. and Zimmermann, K.H., Universal Groebner bases for Binary Linear Code, International Journal of Pure and Applied Mathematics 86(2013), no.2, 345-358.
  • [11] Greuel, G.M. and Pfister, G., A Singular Introduction to Commutative Algebra, Springer-Verlag, Berlin, 2002.
  • [12] Hironaka, H., Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann.Math. 79(1964), 109-326.
  • [13] Mora, T., Pfister, G. and Traverso, C., An introduction to the tangent cone algorithm, Advances in Computing Research 6(1992), 199-270.
  • [14] Sala, M., Mora, T., Perret, L., Sakata, S., and Traverso, C., Groebner Bases, Coding, and Cryptography, Springer, Berlin 2009.
  • [15] Saleemi, M. and Zimmermann, K.H., Groebner Bases for Linear Codes, International Journal of Pure and Applied Mathematics 62(2010), no.4, 481-491.
  • [16] Saleemi, M. and Zimmermann, K.H., Linear Codes as Binomial Ideals, International Journal of Pure and Applied Mathematics 61(2010), no.2, 147-156.

Standard Bases for Linear Codes over Prime Fields

Yıl 2019, , 94 - 101, 30.04.2019

Jean Jacques Ferdinand Randriamiarampanahy Harinaivo Andriatahiny Toussaint Joseph Rabeherimanana

https://doi.org/10.36753/mathenot.559263

Öz

It is known that a linear code can be represented by a binomial ideal. In this paper, we give standard
bases for the ideals in a localization of the multivariate polynomial ring in the case of the linear codes
over prime fields.

Anahtar Kelimeler

Linear code semigroup order Groebner basis local ring standard basis

Kaynakça

  • [1] Adams, W. and Loustaunau, P., An Introduction to Groebner Bases, American Mathematical Society, Vol.3, 1994.
  • [2] Borges-quintana, M., Borges-Trenard, M., Fitzpatrick P. and Martinez-Moro E., Groebner bases and combinatorics for binary codes, Applicable Algebra in Engineering Communication and Computing - AAECC 19(2008), 393-411.
  • [3] Buchberger, B., An Algorithm for Finding the Basis Elements of the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal, PhD thesis, University of Innsbruck, 1965.
  • [4] Cooper, A., Towards a new method of decoding Algebraic codes using Groebner bases, Transactions 10th Army Conf. Appl. Math. Comp. 93(1992), 293-297.
  • [5] Cox, D., Little J. and O’Shea D., Ideals, Varieties, and Algorithms, Springer, 1996.
  • [6] Cox, D., Little J. and O’Shea D., Using Algebraic Geometry, Springer, 1998.
  • [7] Drton, M., Sturmfels B., Sullivan S., Lectures on Algebraic Statistics, Birkhäuser, Basel, 2009.
  • [8] Dück, N. and Zimmermann, K.H., Gröbner bases for perfect binary linear codes, International Journal of Pure and Applied Mathematics 91(2014), no.2, 155-167.
  • [9] Dück, N. and Zimmermann, K.H., Standard Bases for binary Linear Codes, International Journal of Pure and Applied Mathematics 80(2012), no.3, 315-329.
  • [10] Dück, N. and Zimmermann, K.H., Universal Groebner bases for Binary Linear Code, International Journal of Pure and Applied Mathematics 86(2013), no.2, 345-358.
  • [11] Greuel, G.M. and Pfister, G., A Singular Introduction to Commutative Algebra, Springer-Verlag, Berlin, 2002.
  • [12] Hironaka, H., Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann.Math. 79(1964), 109-326.
  • [13] Mora, T., Pfister, G. and Traverso, C., An introduction to the tangent cone algorithm, Advances in Computing Research 6(1992), 199-270.
  • [14] Sala, M., Mora, T., Perret, L., Sakata, S., and Traverso, C., Groebner Bases, Coding, and Cryptography, Springer, Berlin 2009.
  • [15] Saleemi, M. and Zimmermann, K.H., Groebner Bases for Linear Codes, International Journal of Pure and Applied Mathematics 62(2010), no.4, 481-491.
  • [16] Saleemi, M. and Zimmermann, K.H., Linear Codes as Binomial Ideals, International Journal of Pure and Applied Mathematics 61(2010), no.2, 147-156.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Jean Jacques Ferdinand Randriamiarampanahy

Harinaivo Andriatahiny

Toussaint Joseph Rabeherimanana

Yayımlanma Tarihi 30 Nisan 2019
Gönderilme Tarihi 2 Ağustos 2018
Yayımlandığı Sayı Yıl 2019

Kaynak Göster

APA Randriamiarampanahy, J. J. F., Andriatahiny, H., & Rabeherimanana, T. J. (2019). Standard Bases for Linear Codes over Prime Fields. Mathematical Sciences and Applications E-Notes, 7(1), 94-101. https://doi.org/10.36753/mathenot.559263
AMA Randriamiarampanahy JJF, Andriatahiny H, Rabeherimanana TJ. Standard Bases for Linear Codes over Prime Fields. Math. Sci. Appl. E-Notes. Nisan 2019;7(1):94-101. doi:10.36753/mathenot.559263
Chicago Randriamiarampanahy, Jean Jacques Ferdinand, Harinaivo Andriatahiny, ve Toussaint Joseph Rabeherimanana. “Standard Bases for Linear Codes over Prime Fields”. Mathematical Sciences and Applications E-Notes 7, sy. 1 (Nisan 2019): 94-101. https://doi.org/10.36753/mathenot.559263.
EndNote Randriamiarampanahy JJF, Andriatahiny H, Rabeherimanana TJ (01 Nisan 2019) Standard Bases for Linear Codes over Prime Fields. Mathematical Sciences and Applications E-Notes 7 1 94–101.
IEEE J. J. F. Randriamiarampanahy, H. Andriatahiny, ve T. J. Rabeherimanana, “Standard Bases for Linear Codes over Prime Fields”, Math. Sci. Appl. E-Notes, c. 7, sy. 1, ss. 94–101, 2019, doi: 10.36753/mathenot.559263.
ISNAD Randriamiarampanahy, Jean Jacques Ferdinand vd. “Standard Bases for Linear Codes over Prime Fields”. Mathematical Sciences and Applications E-Notes 7/1 (Nisan 2019), 94-101. https://doi.org/10.36753/mathenot.559263.
JAMA Randriamiarampanahy JJF, Andriatahiny H, Rabeherimanana TJ. Standard Bases for Linear Codes over Prime Fields. Math. Sci. Appl. E-Notes. 2019;7:94–101.
MLA Randriamiarampanahy, Jean Jacques Ferdinand vd. “Standard Bases for Linear Codes over Prime Fields”. Mathematical Sciences and Applications E-Notes, c. 7, sy. 1, 2019, ss. 94-101, doi:10.36753/mathenot.559263.
Vancouver Randriamiarampanahy JJF, Andriatahiny H, Rabeherimanana TJ. Standard Bases for Linear Codes over Prime Fields. Math. Sci. Appl. E-Notes. 2019;7(1):94-101.

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