참고문헌
-
T. Abualrub and I. Siap, Constacyclic codes over
$\mathbb{F}_{2}\;+u\mathbb{F}_{2}$ , J. Franklin Inst. 346 (2009), no. 5, 520-529. https://doi.org/10.1016/j.jfranklin.2009.02.001 - G. Castagnoli, J. L. Massey, P. A. Schoeller, and N. von Seemann, On repeated-root cyclic codes, IEEE Trans. Inform. Theory 37 (1991), no. 2, 337-342. https://doi.org/10.1109/18.75249
-
B. Chen, H. Q. Dinh, H. Liu, and L. Wang, Constacyclic codes of length
$2p^{s}$ over$\mathbb{F}_{p}m\;+u\mathbb{F}_{p}m$ , Finite Fields Appl., 37 (2016), 108-130. https://doi.org/10.1016/j.ffa.2015.09.006 -
H. Q. Dinh, Negacyclic codes of length
$2^s$ over Galois rings, IEEE Trans. Inform. Theory 51 (2005), no. 12, 4252-4262. https://doi.org/10.1109/TIT.2005.859284 -
H. Q. Dinh, Constacyclic codes of length
$2^s$ over Galois extension rings of$\mathbb{F}_{2}\;+u\mathbb{F}_{2}$ , IEEE Trans. Inform. Theory 55 (2009), no. 4, 1730-1740. https://doi.org/10.1109/TIT.2009.2013015 -
H. Q. Dinh, Constacyclic codes of length
$p^{s}$ over$\mathbb{F}_{p}m\;+u\mathbb{F}_{p}m$ , J. Algebra 324 (2010), no. 5, 940-950. https://doi.org/10.1016/j.jalgebra.2010.05.027 -
H. Q. Dinh, Repeated-root constacyclic codes of length
$2p^s$ , Finite Fields Appl. 18 (2012), no. 1, 133-143. https://doi.org/10.1016/j.ffa.2011.07.003 -
H. Q. Dinh, Structure of repeated-root constacyclic codes of length
$3p^s$ and their duals, Discrete Math. 313 (2013), no. 9, 983-991. https://doi.org/10.1016/j.disc.2013.01.024 -
H. Q. Dinh, S. Dhompongsa, and S. Sriboonchitta, On constacyclic codes of length
$4p^{s}$ over$\mathbb{F}_{p}m\;+u\mathbb{F}_{p}m$ , Discrete Math. 340 (2017), no. 4, 832-849. https://doi.org/10.1016/j.disc.2016.11.014 -
H. Q. Dinh, Y. Fan, H. Liu, X. Liu, and S. Sriboonchitta, On self-dual constacyclic codes of length
$p^{s}$ over$\mathbb{F}_{p}m\;+u\mathbb{F}_{p}m$ , Discrete Math. 341 (2018), no. 2, 324-335. https://doi.org/10.1016/j.disc.2017.08.044 - H. Q. Dinh and S. R. Lopez-Permouth, Cyclic and negacyclic codes over nite chain rings, IEEE Trans. Inform. Theory 50 (2004), no. 8, 1728-1744. https://doi.org/10.1109/TIT.2004.831789
-
H. Q. Dinh, B. T. Nguyen, and S. Sriboonchitta, Negacyclic codes of length
$4p^{s}$ over$\mathbb{F}_{p}m\;+u\mathbb{F}_{p}m$ and their duals, Discrete Math. 341 (2018), no. 4, 1055-1071. https://doi.org/10.1016/j.disc.2017.12.019 -
H. Q. Dinh, B. T. Nguyen, S. Sriboonchitta, and T. M. Vo, On
$({\alpha}\;+\;u{\beta})$ -constacyclic codes of length$4p^{s}$ over$\mathbb{F}_{p}m\;+u\mathbb{F}_{p}m*$ , J. Algebra Appl. 18 (2019), no. 2, 1950023, 16 pp. https://doi.org/10.1142/S0219498819500233 -
H. Q. Dinh, L. Wang, and S. Zhu, Negacyclic codes of length
$2p^{s}$ over$\mathbb{F}_{p}m\;+u\mathbb{F}_{p}m$ , Finite Fields Appl. 31 (2015), 178-201. https://doi.org/10.1016/j.ffa.2014.09.003 - G. Falkner, B. Kowol, W. Heise, and E. Zehendner, On the existence of cyclic optimal codes, Atti Sem. Mat. Fis. Univ. Modena 28 (1979), no. 2, 326-341.
-
K. Guenda and T. A. Gulliver, Construction of cyclic codes over
$\mathbb{F}_{2}\;+u\mathbb{F}_{2}$ for DNA computing, Appl. Algebra Engrg. Comm. Comput. 24 (2013), no. 6, 445-459. https://doi.org/10.1007/s00200-013-0188-x - J. H. van Lint, Repeated-root cyclic codes, IEEE Trans. Inform. Theory 37 (1991), no. 2, 343-345. https://doi.org/10.1109/18.75250
-
X. Liu and X. Xu, Cyclic and negacyclic codes of length
$2p^{s}$ over$\mathbb{F}_{p}m\;+u\mathbb{F}_{p}m$ , Acta Math. Sci. Ser. B (Engl. Ed.) 34 (2014), no. 3, 829-839. https://doi.org/10.1016/S0252-9602(14)60053-9 - R. M. Roth and G. Seroussi, On cyclic MDS codes of length q over GF(q), IEEE Trans. Inform. Theory 32 (1986), no. 2, 284-285. https://doi.org/10.1109/TIT.1986.1057151