[1] |
Goppa V D. Codes on algebraic curves. Soviet Mathematics Doklady, 1981, 24 (1): 170–172.
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[2] |
Tsfasman M A, Vlăduţ S G, Zink T. Modular curves, Shimura curves, and Goppa codes, better than the Varshamov–Gilbert bound. Mathematische Nachrichten, 1982, 109: 21–28. doi: 10.1002/mana.19821090103
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[3] |
Mesnager S, Tang C, Qi Y. Complementary dual algebraic geometry codes. IEEE Transactions on Information Theory, 2018, 64 (4): 2390–2397. doi: 10.1109/TIT.2017.2766075
|
[4] |
Jin L, Kan H. Self-dual near MDS codes from elliptic curves. IEEE Transactions on Information Theory, 2019, 65 (4): 2166–2170. doi: 10.1109/TIT.2018.2880913
|
[5] |
Barg A, Tamo I, Vlăduţ S. Locally recoverable codes on algebraic curves. IEEE Transactions on Information Theory, 2017, 63 (8): 4928–4939. doi: 10.1109/TIT.2017.2700859
|
[6] |
Li X, Ma L, Xing C. Optimal locally repairable codes via elliptic curves. IEEE Transactions on Information Theory, 2019, 65 (1): 108–117. doi: 10.1109/TIT.2018.2844216
|
[7] |
Ma L, Xing C. The group structures of automorphism groups of elliptic curves over finite fields and their applications to optimal locally repairable codes. Journal of Combinatorial Theory, Series A, 2023, 193: 105686. doi: 10.1016/j.jcta.2022.105686
|
[8] |
Massey J L. Linear codes with complementary duals. Discrete Mathematics, 1992, 106–107: 337–342. doi: 10.1016/0012-365X(92)90563-U
|
[9] |
Carlet C, Guilley S. Complementary dual codes for counter-measures to side-channel attacks. In: Coding Theory and Applications. Cham, Switzerland: Springer, 2015.
|
[10] |
Guenda K, Jitman S, Gulliver T A. Constructions of good entanglement-assisted quantum error correcting codes. Designs, Codes and Cryptography, 2018, 86: 121–136. doi: 10.1007/s10623-017-0330-z
|
[11] |
Carlet C, Mesnager S, Tang C, et al. Euclidean and Hermitian LCD MDS codes. Designs, Codes and Cryptography, 2018, 86: 2605–2618. doi: 10.1007/s10623-018-0463-8
|
[12] |
Chen B, Liu H. New constructions of MDS codes with complementary duals. IEEE Transactions on Information Theory, 2018, 64 (8): 5776–5782. doi: 10.1109/TIT.2017.2748955
|
[13] |
Jin L. Construction of MDS codes with complementary duals. IEEE Transactions on Information Theory, 2017, 63 (5): 2843–2847. doi: 10.1109/TIT.2016.2644660
|
[14] |
Beelen P, Jin L. Explicit MDS codes with complementary duals. IEEE Transactions on Information Theory, 2018, 64 (11): 7188–7193. doi: 10.1109/TIT.2018.2816934
|
[15] |
Liu H, Liu S. Construction of MDS twisted Reed–Solomon codes and LCD MDS codes. Designs, Codes and Cryptography, 2021, 89: 2051–2065. doi: 10.1007/s10623-021-00899-z
|
[16] |
Shi X, Yue Q, Yang S. New LCD MDS codes constructed from generalized Reed–Solomon codes. Journal of Algebra and Its Applications, 2018, 18 (8): 1950150. doi: 10.1142/S0219498819501500
|
[17] |
Fan Y, Zhang L. Galois self-dual constacyclic codes. Designs, Codes and Cryptography, 2017, 84: 473–492. doi: 10.1007/s10623-016-0282-8
|
[18] |
Liu X, Fan Y, Liu H. Galois LCD codes over finite fields. Finite Fields and Their Applications, 2018, 49: 227–242. doi: 10.1016/j.ffa.2017.10.001
|
[19] |
Cao M. MDS Codes with Galois hulls of arbitrary dimensions and the related entanglement-assisted quantum error correction. IEEE Transactions on Information Theory, 2021, 67 (12): 7964–7984. doi: 10.1109/TIT.2021.3117562
|
[20] |
Cao M, Yang J. Intersections of linear codes and related MDS codes with new Galois hulls. arXiv: 2210.05551, 2022.
|
[21] |
Fang X, Jin R, Luo J, et al. New Galois hulls of GRS codes and application to EAQECCs. Cryptography and Communications, 2022, 14: 145–159. doi: 10.1007/s12095-021-00525-8
|
[22] |
Li Y, Zhu S, Li P. On MDS codes with Galois hulls of arbitrary dimensions. Cryptography and Communications, 2023, 15: 565–587. doi: 10.1007/s12095-022-00621-3
|
[23] |
Wu Y, Li C, Yang S. New Galois hulls of generalized Reed–Solomon codes. Finite Fields and Their Applications, 2022, 83: 102084. doi: 10.1016/j.ffa.2022.102084
|
[24] |
Stichtenoth H. Algebraic Function Fields and Codes. Berlin: Springer-Verlag, 2009.
|
[25] |
Lang S. Algebra. New York: Springer-Verlag, 2002.
|
[1] |
Goppa V D. Codes on algebraic curves. Soviet Mathematics Doklady, 1981, 24 (1): 170–172.
|
[2] |
Tsfasman M A, Vlăduţ S G, Zink T. Modular curves, Shimura curves, and Goppa codes, better than the Varshamov–Gilbert bound. Mathematische Nachrichten, 1982, 109: 21–28. doi: 10.1002/mana.19821090103
|
[3] |
Mesnager S, Tang C, Qi Y. Complementary dual algebraic geometry codes. IEEE Transactions on Information Theory, 2018, 64 (4): 2390–2397. doi: 10.1109/TIT.2017.2766075
|
[4] |
Jin L, Kan H. Self-dual near MDS codes from elliptic curves. IEEE Transactions on Information Theory, 2019, 65 (4): 2166–2170. doi: 10.1109/TIT.2018.2880913
|
[5] |
Barg A, Tamo I, Vlăduţ S. Locally recoverable codes on algebraic curves. IEEE Transactions on Information Theory, 2017, 63 (8): 4928–4939. doi: 10.1109/TIT.2017.2700859
|
[6] |
Li X, Ma L, Xing C. Optimal locally repairable codes via elliptic curves. IEEE Transactions on Information Theory, 2019, 65 (1): 108–117. doi: 10.1109/TIT.2018.2844216
|
[7] |
Ma L, Xing C. The group structures of automorphism groups of elliptic curves over finite fields and their applications to optimal locally repairable codes. Journal of Combinatorial Theory, Series A, 2023, 193: 105686. doi: 10.1016/j.jcta.2022.105686
|
[8] |
Massey J L. Linear codes with complementary duals. Discrete Mathematics, 1992, 106–107: 337–342. doi: 10.1016/0012-365X(92)90563-U
|
[9] |
Carlet C, Guilley S. Complementary dual codes for counter-measures to side-channel attacks. In: Coding Theory and Applications. Cham, Switzerland: Springer, 2015.
|
[10] |
Guenda K, Jitman S, Gulliver T A. Constructions of good entanglement-assisted quantum error correcting codes. Designs, Codes and Cryptography, 2018, 86: 121–136. doi: 10.1007/s10623-017-0330-z
|
[11] |
Carlet C, Mesnager S, Tang C, et al. Euclidean and Hermitian LCD MDS codes. Designs, Codes and Cryptography, 2018, 86: 2605–2618. doi: 10.1007/s10623-018-0463-8
|
[12] |
Chen B, Liu H. New constructions of MDS codes with complementary duals. IEEE Transactions on Information Theory, 2018, 64 (8): 5776–5782. doi: 10.1109/TIT.2017.2748955
|
[13] |
Jin L. Construction of MDS codes with complementary duals. IEEE Transactions on Information Theory, 2017, 63 (5): 2843–2847. doi: 10.1109/TIT.2016.2644660
|
[14] |
Beelen P, Jin L. Explicit MDS codes with complementary duals. IEEE Transactions on Information Theory, 2018, 64 (11): 7188–7193. doi: 10.1109/TIT.2018.2816934
|
[15] |
Liu H, Liu S. Construction of MDS twisted Reed–Solomon codes and LCD MDS codes. Designs, Codes and Cryptography, 2021, 89: 2051–2065. doi: 10.1007/s10623-021-00899-z
|
[16] |
Shi X, Yue Q, Yang S. New LCD MDS codes constructed from generalized Reed–Solomon codes. Journal of Algebra and Its Applications, 2018, 18 (8): 1950150. doi: 10.1142/S0219498819501500
|
[17] |
Fan Y, Zhang L. Galois self-dual constacyclic codes. Designs, Codes and Cryptography, 2017, 84: 473–492. doi: 10.1007/s10623-016-0282-8
|
[18] |
Liu X, Fan Y, Liu H. Galois LCD codes over finite fields. Finite Fields and Their Applications, 2018, 49: 227–242. doi: 10.1016/j.ffa.2017.10.001
|
[19] |
Cao M. MDS Codes with Galois hulls of arbitrary dimensions and the related entanglement-assisted quantum error correction. IEEE Transactions on Information Theory, 2021, 67 (12): 7964–7984. doi: 10.1109/TIT.2021.3117562
|
[20] |
Cao M, Yang J. Intersections of linear codes and related MDS codes with new Galois hulls. arXiv: 2210.05551, 2022.
|
[21] |
Fang X, Jin R, Luo J, et al. New Galois hulls of GRS codes and application to EAQECCs. Cryptography and Communications, 2022, 14: 145–159. doi: 10.1007/s12095-021-00525-8
|
[22] |
Li Y, Zhu S, Li P. On MDS codes with Galois hulls of arbitrary dimensions. Cryptography and Communications, 2023, 15: 565–587. doi: 10.1007/s12095-022-00621-3
|
[23] |
Wu Y, Li C, Yang S. New Galois hulls of generalized Reed–Solomon codes. Finite Fields and Their Applications, 2022, 83: 102084. doi: 10.1016/j.ffa.2022.102084
|
[24] |
Stichtenoth H. Algebraic Function Fields and Codes. Berlin: Springer-Verlag, 2009.
|
[25] |
Lang S. Algebra. New York: Springer-Verlag, 2002.
|