Research Article
BibTex RIS Cite

Ternary maximal self-orthogonal codes of lengths $21,22$ and $23$

Year 2018, , 1 - 4, 15.01.2018
https://doi.org/10.13069/jacodesmath.327391

Abstract

We give a classification
of ternary maximal self-orthogonal codes of lengths $21,22$ and $23$.
This completes a classification
of ternary maximal self-orthogonal codes of lengths up to $24$.

References

  • [1] W. Bosma, J. Cannon, C. Playoust, The Magma algebra system I: The user language, J. Symb. Comput. 24(3–4) (1997) 235–265.
  • [2] J. Conway, V. Pless, N. J. A. Sloane, Self–dual codes over GF(3) and GF(4) of length not exceeding 16, IEEE Trans. Inform. Theory 25(3) (1979) 312–322.
  • [3] M. Harada, A. Munemasa, A complete classification of ternary self–dual codes of length 24, J. Combin. Theory Ser. A 116(5) (2009) 1063–1072.
  • [4] M. Harada, A. Munemasa, On the classification of weighing matrices and self–orthogonal codes, J. Combin. Des. 20(1) (2012) 40–57.
  • [5] M. Harada, A. Munemasa, Database of Ternary Maximal Self–Orthogonal Codes, http://www.math. is.tohoku.ac.jp/~munemasa/research/codes/mso3.htm.
  • [6] C. W. H. Lam, L. Thiel, A. Pautasso, On ternary codes generated by Hadamard matrices of order 24, Congr. Numer. 89 (1992) 7–14.
  • [7] J. Leon, V. Pless, N. J. A. Sloane, On ternary self–dual codes of length 24, IEEE Trans. Inform. Theory 27(2) (1981) 176–180.
  • [8] C. L. Mallows, V. Pless, N. J. A. Sloane, Self–dual codes over GF(3), SIAM J. Appl. Math. 31(4) (1976) 649–666.
  • [9] V. Pless, N. J. A. Sloane, H. N. Ward, Ternary codes of minimum weight 6 and the classification of the self–dual codes of length 20, IEEE Trans. Inform. Theory 26(3) (1980) 305–316.
Year 2018, , 1 - 4, 15.01.2018
https://doi.org/10.13069/jacodesmath.327391

Abstract

References

  • [1] W. Bosma, J. Cannon, C. Playoust, The Magma algebra system I: The user language, J. Symb. Comput. 24(3–4) (1997) 235–265.
  • [2] J. Conway, V. Pless, N. J. A. Sloane, Self–dual codes over GF(3) and GF(4) of length not exceeding 16, IEEE Trans. Inform. Theory 25(3) (1979) 312–322.
  • [3] M. Harada, A. Munemasa, A complete classification of ternary self–dual codes of length 24, J. Combin. Theory Ser. A 116(5) (2009) 1063–1072.
  • [4] M. Harada, A. Munemasa, On the classification of weighing matrices and self–orthogonal codes, J. Combin. Des. 20(1) (2012) 40–57.
  • [5] M. Harada, A. Munemasa, Database of Ternary Maximal Self–Orthogonal Codes, http://www.math. is.tohoku.ac.jp/~munemasa/research/codes/mso3.htm.
  • [6] C. W. H. Lam, L. Thiel, A. Pautasso, On ternary codes generated by Hadamard matrices of order 24, Congr. Numer. 89 (1992) 7–14.
  • [7] J. Leon, V. Pless, N. J. A. Sloane, On ternary self–dual codes of length 24, IEEE Trans. Inform. Theory 27(2) (1981) 176–180.
  • [8] C. L. Mallows, V. Pless, N. J. A. Sloane, Self–dual codes over GF(3), SIAM J. Appl. Math. 31(4) (1976) 649–666.
  • [9] V. Pless, N. J. A. Sloane, H. N. Ward, Ternary codes of minimum weight 6 and the classification of the self–dual codes of length 20, IEEE Trans. Inform. Theory 26(3) (1980) 305–316.
There are 9 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Makoto Araya This is me 0000-0002-9935-038X

Masaaki Harada This is me 0000-0002-2748-6456

Yuichi Suzuki This is me

Publication Date January 15, 2018
Published in Issue Year 2018

Cite

APA Araya, M., Harada, M., & Suzuki, Y. (2018). Ternary maximal self-orthogonal codes of lengths $21,22$ and $23$. Journal of Algebra Combinatorics Discrete Structures and Applications, 5(1), 1-4. https://doi.org/10.13069/jacodesmath.327391
AMA Araya M, Harada M, Suzuki Y. Ternary maximal self-orthogonal codes of lengths $21,22$ and $23$. Journal of Algebra Combinatorics Discrete Structures and Applications. January 2018;5(1):1-4. doi:10.13069/jacodesmath.327391
Chicago Araya, Makoto, Masaaki Harada, and Yuichi Suzuki. “Ternary Maximal Self-Orthogonal Codes of Lengths $21,22$ and $23$”. Journal of Algebra Combinatorics Discrete Structures and Applications 5, no. 1 (January 2018): 1-4. https://doi.org/10.13069/jacodesmath.327391.
EndNote Araya M, Harada M, Suzuki Y (January 1, 2018) Ternary maximal self-orthogonal codes of lengths $21,22$ and $23$. Journal of Algebra Combinatorics Discrete Structures and Applications 5 1 1–4.
IEEE M. Araya, M. Harada, and Y. Suzuki, “Ternary maximal self-orthogonal codes of lengths $21,22$ and $23$”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 5, no. 1, pp. 1–4, 2018, doi: 10.13069/jacodesmath.327391.
ISNAD Araya, Makoto et al. “Ternary Maximal Self-Orthogonal Codes of Lengths $21,22$ and $23$”. Journal of Algebra Combinatorics Discrete Structures and Applications 5/1 (January 2018), 1-4. https://doi.org/10.13069/jacodesmath.327391.
JAMA Araya M, Harada M, Suzuki Y. Ternary maximal self-orthogonal codes of lengths $21,22$ and $23$. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018;5:1–4.
MLA Araya, Makoto et al. “Ternary Maximal Self-Orthogonal Codes of Lengths $21,22$ and $23$”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 5, no. 1, 2018, pp. 1-4, doi:10.13069/jacodesmath.327391.
Vancouver Araya M, Harada M, Suzuki Y. Ternary maximal self-orthogonal codes of lengths $21,22$ and $23$. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018;5(1):1-4.