پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 43 |
| تعداد شماره‌ها | 1,675 |
| تعداد مقالات | 13,674 |
| تعداد مشاهده مقاله | 31,688,821 |
| تعداد دریافت فایل اصل مقاله | 12,517,540 |
Linear codes resulting from finite group actions | ||
| Transactions on Combinatorics | ||
| مقاله 8، دوره 11، شماره 4، اسفند 2022، صفحه 335-343 اصل مقاله (472.79 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2022.126254.1786 | ||
| نویسنده | ||
| Driss Harzalla* | ||
| Department of Mathematics, University of Cadi Ayyad, Box 63 46000 Route Sidi Bouzid, Safi, Morocco | ||
| چکیده | ||
| In this article, we use group action theory to define some important ternary linear codes. Some of these codes are self-orthogonal having a minimum distance achieving the lower bound in the previous records. Then, we define two new codes sharing the same automorphism group isomorphic to $C_2 \times M_{11}$ where $M_{11}$ is the Sporadic Mathieu group and $C_{2}$ is a cyclic group of two elements. We also study the natural action of the general linear group $GL (k, 2) $ on the vector space $F_2 ^ k$ to characterize Hamming codes $H_k (2) $ and their automorphism group. | ||
| کلیدواژه‌ها | ||
| Linear Code automorphism؛ Group Actions؛ Hamming codes؛ simplex codes | ||
| مراجع | ||
|
[1] W. Cary Huffman, Codes and groups, Handbook of coding theory, I, II, North-Holland, Amsterdam, (1998) 1345– 1440. [2] F. J. MacWilliams, Permutation decoding of systematic codes, Bell System Tech. J., 43 (1964) 485–505.
[3] L. M. G. M. Tolhuizen and W. J. van, Gils A large automorphism group decreases the number of computations in the construction of an optimal encoder/decoder pair for a linear block code, IEEE Trans. Inf. Theory, 34 (1988) 333–338. [4] J. D. Key, Permutation decoding for codes from designs, finite geometries and graphs, Information security, cod- ing theory and related combinatorics, 172–201, NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur., 29, IOS, Amsterdam, 2011. [5] H.-J. Kroll and R. Vincenti, PD-sets for the codes related to some classical varieties, Discrete Math., 301 (2005) 89–105. [6] G. Chen and R. Li, Ternary self-orthogonal codes of dual distance three and ternary quantum codes of distance three, Des. Codes, Cryptogr, 69 (2013) 53–63. [7] F. Liang, Self-orthogonal codes with dual distance three and quantum codes with distance three over F5 , Quantum Inf. Process., 12 (2013) 3617–3623. [8] F. De Clerck and M. Delanote, Two-weight codes, partial geometries and Steiner systems, Des. Codes Cryptogr, 21 (2000) 87–98. [9] Ph. Delsarte, Weights of linear codes and strongly regular normed spaces, Discrete Math., 3 (1972) 47–64.
[10] R. Calderbank and W. M. Kantor, The geometry of two-weight codes, Bull. London Math. Soc., 18 (1986) 97–122.
[11] K. Ding and C. Ding, A class of two-weight and three-weight codes and their applications in secret sharing, IEEE Trans. Inform. Theory, 61 (2015) 5835–5842. [12] W. C. Huffman and V. Pless, Fundamentals of error-correcting codes, Cambridge University Press, Cambridge, 2003.
[13] V. Pless, Introduction to the theory of error-correcting codes, Third edition. Wiley-Interscience Series in Discrete Mathematics and Optimization, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1998. [14] D. Joyner and A. Ksir, Automorphism groups of some AG codes, IEEE Trans. Inform. Theory, 52 (2006) 3325–3329.
[15] F. J. MacWilliams and N. J. Sloane, The theory of error-correcting codes, I., II., North-Holland Mathematical Library, 16, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. [16] M. Grassl, Bounds on the minimum distance of linear codes and quantum codes. Online available at http:///www. codetables.de.Accessedon2019-10-05. [17] https://www.gap-system.org | ||
|
آمار تعداد مشاهده مقاله: 516 تعداد دریافت فایل اصل مقاله: 641 |
||