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One–generator quasi–abelian codes revisited

Yıl 2017, , 49 - 60, 11.01.2017
https://doi.org/10.13069/jacodesmath.09585

Öz

The class of 1-generator quasi-abelian codes over finite fields is revisited. Alternative and explicit
characterization and enumeration of such codes are given. An algorithm to find all 1-generator
quasi-abelian codes is provided. Two 1-generator quasi-abelian codes whose minimum distances are
improved from Grassl’s online table are presented.

Kaynakça

  • [1] S. D. Berman, Semi–simple cyclic and abelian codes. II, Kibernetika 3(3) (1967) 21–30.
  • [2] S. D. Berman, On the theory of group codes, Kibernetika 3(1) (1967) 31–39.
  • [3] W. Bosma, J. Cannon, C. Playoust, The Magma algebra system I: The user language, J. Symbolic Comput. 24(3–4) (1997) 235–265.
  • [4] C. Ding, D. R. Kohel, S. Ling, Split group codes, IEEE Trans. Inform. Theory 46(2) (2000) 485–495.
  • [5] M. Grassl, Bounds on the minimum distance of linear codes and quantum codes, Online available at http://www.codetables.de, Accessed on 2015-10-09.
  • [6] S. Jitman, Generator matrices for new quasi–abelian codes, Online available at https://sites.google.com/site/quasiabeliancodes, Accessed on 2015-10-09.
  • [7] S. Jitman, S. Ling, Quasi–abelian codes, Des. Codes Cryptogr. 74(3) (2015) 511–531.
  • [8] K. Lally, P. Fitzpatrick, Algebraic structure of quasicyclic codes, Discrete Appl. Math. 111(1–2) (2001) 157–175.
  • [9] S. Ling, P. Solé, On the algebraic structure of quasi–cyclic codes I: Finite fields, IEEE Trans. Inform. Theory 47(7) (2001) 2751–2760.
  • [10] S. Ling, P. Solé, Good self–dual quasi–cyclic codes exist, IEEE Trans. Inform. Theory 49(4) (2003) 1052–1053.
  • [11] S. Ling, P. Solé, On the algebraic structure of quasi–cyclic codes III: Generator theory, IEEE Trans. Inform. Theory 51(7) (2005) 2692–2700.
  • [12] F. J. MacWilliams, N. J. A. Sloane, The Theory of Error–Correcting Codes, Amsterdam, The Netherlands: North–Holland, 1977.
  • [13] J. Pei, X. Zhang, 1-generator quasi–cyclic codes, J. Syst. Sci. Complex. 20(4) (2007) 554–561.
  • [14] G. E. Seguin, A class of 1-generator quasi–cyclic codes, IEEE Trans. Inform. Theory 50(8) (2004) 1745–1753.
  • [15] S. K. Wasan, Quasi abelian codes, Pub. Inst. Math. 21(35) (1977) 201–206.
Yıl 2017, , 49 - 60, 11.01.2017
https://doi.org/10.13069/jacodesmath.09585

Öz

Kaynakça

  • [1] S. D. Berman, Semi–simple cyclic and abelian codes. II, Kibernetika 3(3) (1967) 21–30.
  • [2] S. D. Berman, On the theory of group codes, Kibernetika 3(1) (1967) 31–39.
  • [3] W. Bosma, J. Cannon, C. Playoust, The Magma algebra system I: The user language, J. Symbolic Comput. 24(3–4) (1997) 235–265.
  • [4] C. Ding, D. R. Kohel, S. Ling, Split group codes, IEEE Trans. Inform. Theory 46(2) (2000) 485–495.
  • [5] M. Grassl, Bounds on the minimum distance of linear codes and quantum codes, Online available at http://www.codetables.de, Accessed on 2015-10-09.
  • [6] S. Jitman, Generator matrices for new quasi–abelian codes, Online available at https://sites.google.com/site/quasiabeliancodes, Accessed on 2015-10-09.
  • [7] S. Jitman, S. Ling, Quasi–abelian codes, Des. Codes Cryptogr. 74(3) (2015) 511–531.
  • [8] K. Lally, P. Fitzpatrick, Algebraic structure of quasicyclic codes, Discrete Appl. Math. 111(1–2) (2001) 157–175.
  • [9] S. Ling, P. Solé, On the algebraic structure of quasi–cyclic codes I: Finite fields, IEEE Trans. Inform. Theory 47(7) (2001) 2751–2760.
  • [10] S. Ling, P. Solé, Good self–dual quasi–cyclic codes exist, IEEE Trans. Inform. Theory 49(4) (2003) 1052–1053.
  • [11] S. Ling, P. Solé, On the algebraic structure of quasi–cyclic codes III: Generator theory, IEEE Trans. Inform. Theory 51(7) (2005) 2692–2700.
  • [12] F. J. MacWilliams, N. J. A. Sloane, The Theory of Error–Correcting Codes, Amsterdam, The Netherlands: North–Holland, 1977.
  • [13] J. Pei, X. Zhang, 1-generator quasi–cyclic codes, J. Syst. Sci. Complex. 20(4) (2007) 554–561.
  • [14] G. E. Seguin, A class of 1-generator quasi–cyclic codes, IEEE Trans. Inform. Theory 50(8) (2004) 1745–1753.
  • [15] S. K. Wasan, Quasi abelian codes, Pub. Inst. Math. 21(35) (1977) 201–206.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Makaleler
Yazarlar

Somphong Jitman

Patanee Udomkavanich Bu kişi benim

Yayımlanma Tarihi 11 Ocak 2017
Yayımlandığı Sayı Yıl 2017

Kaynak Göster

APA Jitman, S., & Udomkavanich, P. (2017). One–generator quasi–abelian codes revisited. Journal of Algebra Combinatorics Discrete Structures and Applications, 4(1), 49-60. https://doi.org/10.13069/jacodesmath.09585
AMA Jitman S, Udomkavanich P. One–generator quasi–abelian codes revisited. Journal of Algebra Combinatorics Discrete Structures and Applications. Ocak 2017;4(1):49-60. doi:10.13069/jacodesmath.09585
Chicago Jitman, Somphong, ve Patanee Udomkavanich. “One–generator quasi–abelian Codes Revisited”. Journal of Algebra Combinatorics Discrete Structures and Applications 4, sy. 1 (Ocak 2017): 49-60. https://doi.org/10.13069/jacodesmath.09585.
EndNote Jitman S, Udomkavanich P (01 Ocak 2017) One–generator quasi–abelian codes revisited. Journal of Algebra Combinatorics Discrete Structures and Applications 4 1 49–60.
IEEE S. Jitman ve P. Udomkavanich, “One–generator quasi–abelian codes revisited”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 4, sy. 1, ss. 49–60, 2017, doi: 10.13069/jacodesmath.09585.
ISNAD Jitman, Somphong - Udomkavanich, Patanee. “One–generator quasi–abelian Codes Revisited”. Journal of Algebra Combinatorics Discrete Structures and Applications 4/1 (Ocak 2017), 49-60. https://doi.org/10.13069/jacodesmath.09585.
JAMA Jitman S, Udomkavanich P. One–generator quasi–abelian codes revisited. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017;4:49–60.
MLA Jitman, Somphong ve Patanee Udomkavanich. “One–generator quasi–abelian Codes Revisited”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 4, sy. 1, 2017, ss. 49-60, doi:10.13069/jacodesmath.09585.
Vancouver Jitman S, Udomkavanich P. One–generator quasi–abelian codes revisited. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017;4(1):49-60.