Citation: | YAO Ting, ZHU Shixin, KAI Xiaoshan, “Asymptotically Good Additive Cyclic Codes,” Chinese Journal of Electronics, vol. 29, no. 5, pp. 859-864, 2020, doi: 10.1049/cje.2020.05.013 |
R. R. Varshamov, "Estimate of the number of signals in error correcting codes", Dokl. Akad. Nauk SSSR, Vol.117, No.5, pp.739-741, 1957.
|
L. M. J. Bazzi and S. K. Mitter, "Some randomized code constructions from group actions", IEEE Trans. Inform. Theory, Vol.52, No.7, pp.3210-3219, 2006.
|
C. L. Chen, W. W. Peterson and E. J. Weldon, "Some results on quasi-cyclic codes", Inf. Control., Vol.15, No.5, pp.407-423, 1969.
|
V. V. Chepyzhov, "New lower bounds for minimum distance of linear quasi-cyclic and almost linear cyclic codes", Problemy Peredachi Inform., Vol.28, No.1, pp.39-51, 1992.
|
C. Martinez-Perez and W. Willems, "Is the class of cyclic codes asymptotically good?", IEEE Trans. Inform. Theory, Vol.52, No. 2, pp.696-700, 2006.
|
A. Alahmadi, C. Güneri, H. Shoaib, et al., "Long quasipolycyclic t-CIS codes", Adv. Math Commun., Vol.2, No.1, pp.189-198, 2018.
|
M. J. Shi, R. S. Wu and P. Solé, "Asymptotically good additive cyclic codes exist", IEEE Communications Letters, Vol.22, No.10, pp.1980-1983, 2018.
|
M.J. Shi, D.T. Huang, L. Sok, et al., "Double circulant LCD codes over Z4", Finite Fields and Their Applications, Vol.58, pp.133-144, 2019.
|
M. J. Shi, L. Q. Qian and P. Solé, "On self-dual negacirculant codes of index two and four", Designs, Codes and Cryptography, Vol.86, pp. 2485-2494, 2018.
|
S. Ling and P. Solé, "Good self-dual quasi-cyclic codes exist", IEEE Trans. Inform. Theory, Vol.49, No.4, pp.1052-1053, 2003.
|
M. J. Shi, L. Q. Qian, Y. Liu, et al., " Good self-dual generalized quasi-cyclic codes exist", Information Processing Letters, Vol.118, pp.21-24, 2017.
|
T. Yao and S. X. Zhu, "ZpZps-additive cyclic codes are asymptotically good", Cryptography and Communications, DOI:10.1007/s12095-019-00397-z, 2019.
|
P. Delsarte, "An Algebraic Approach to Association Schemes of Coding Theory", ser. Philips Res. Rep., Supplement, 1973.
|
T. Abualrub, I. Siap and H. Aydin, "Z2Z4", IEEE Transactions on Information Theory, Vol.60, No.3, pp.1508-1514, 2014.
|
B. Srinivasulu and M. Bhaintwal, "Z2(Z2+ uZ2)-Additive cyclic codes and their duals', Discrete Mathematics Algorithms and Applications, Vol.8, No.2, DOI:10.1142/S1793830916500270, 2016.
|
M.J. Shi, L. Q. Qian, L. Sok, et al., "On constacyclic codes over Z4[u]/2-1> and their Gray images", Finite Fields and Their Applications, Vol.45, pp.86-95, 2017.
|
Database of Z4 codes, http://www.z4codes.info,2016-9-3.
|
H.L. Liu, "Three questions about quasi-cyclic codes and constacyclic codes", Ph.D. Thesis, Central China Normal University, Wuhan, China, 2018. (in Chinese)
|
I. Aydogdu, T. Abualrub and I. Siap, "On Z2Z2[u]-additive codes", Int. J. Comput. Math., Vol.92, No.9, pp.1806-1814, 2015.
|
Y. Fan and H. L. Liu, "Double circulant matrices", Linear and Multil. Algebra, Vol.66, No. 10, pp.2119-2137, 2018.
|