有限域上常循環(huán)厄密特對(duì)偶包含碼及其應(yīng)用
doi: 10.11999/JEIT170735
基金項(xiàng)目:
國(guó)家自然科學(xué)基金(61772168, 61572168),安徽省自然科學(xué)基金(1508085SQA198, 1708085QA01)
Constacyclic Hermitian Dual-containing Codes over Finite Fields and Their Application
Funds:
The National Natural Science Foundation of China (61772168, 61572168), The Natural Science Found of Anhui Province (1508085SQA198, 1708085QA01)
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摘要: 該文研究了有限域GF(q2)上長(zhǎng)度為(q2m-1)/(q2-1)的常循環(huán)碼。給出一類(lèi)常循環(huán)碼是厄米特對(duì)偶包含碼的一個(gè)充要條件,并確定了這類(lèi)常循環(huán)厄米特對(duì)偶包含碼的參數(shù)。利用厄米特構(gòu)造,得到了比量子BCH碼參數(shù)更好的量子糾錯(cuò)碼。
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關(guān)鍵詞:
- 量子碼 /
- 厄米特構(gòu)造 /
- 常循環(huán)碼 /
- 分圓陪集
Abstract: In this paper, constacyclic codes over the finite fieldGF(q2) of length(q2m-1)/(q2-1) are studied. A sufficient and necessary condition for a class of constacyclic codes to be Hermitian dual-containing codes is given, and the parameters of this class of constacyclic codes are determined. Using Hermitian construction, the obtained quantum codes, are better than the parameters of quantum BCH codes.-
Key words:
- Quantum codes /
- Hermitian construction /
- Constacyclic codes /
- Cyclotomic cosets
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CALDERBANK A R, RAINS E M, SHOR P W, et al. Quantum error correction via codes over [J]. IEEE Transactions on Information Theory, 1998, 44(4): 1369-1387. doi: 10.1109/18.681315. ASHIKHMIN A and KNILL E. Nonbinary quantum stabilizer codes[J]. IEEE Transactions on Information Theory, 2001, 47(7): 3065-3072. doi: 10.1109/18.959298. ALY S A, KLAPPENECKER A, and SARVEPALLI P K. On quantum and classical BCH codes[J]. IEEE Transactions on Information Theory, 2007, 53(3): 1183-1188. doi: 10.1109/ TIT.2006.890730. MA Z, LU X, FENG K, et al. On non-binary quantum codes[C]. International Conference on Theory and Applications of Models of Computation, Berlin Heidelberg, 2006: 675-683. doi: 10.1007/1175 0321_63. XU Y, MA Z, and ZHANG C. On classical BCH codes and quantum BCH codes[J]. Journal of Electronics, 2009, 26(1): 64-70. doi: 10.1007/s11767-007-0120-2. GUARDIA G G L. New families of asymmetric quantum BCH codes[J]. Quantum Information and Computation, 2011, 11(3): 239-252. TANG Y, ZHU S, KAI X, et al. New quantum codes from dual-containing cyclic codes over finite fings[J]. Quantum Information Processing, 2016, 15(11): 4489-4500. doi: 10.1007/s11128-016-1426-5. GUARDIA G G L. Quantum codes defived from cyclic codes[J]. International Journal of Theoretical Physics, 2017, 56(8): 2479-2484. doi: 10.1007/s10773-017 -3399-2. GUARDIA G G L. On optimal constacyclic codes[J]. Linear Algebra and Its Applications, 2016, 496: 594-610. doi: 10.1016 /j.laa.2016.02.014. LIN X. Quantum cyclic and constacyclic codes[J]. IEEE Transactions on Information Theory, 2004, 50(3): 547-549. doi: 10.1109/TIT.2004.825502. KAI X, ZHU S, and TANG Y. Quantum negacyclic codes[J]. Physical Review A, 2013, 88: 012326. doi: 10.1103/PhysRevA. 88.012326. XU G, LI R, GUO L, et al. New quantum codes constructed from quaternary BCH codes[J]. Quantum Information Processing, 2016, 15(10): 4099-4116. doi: 10. 1007/s11128- 016-1397-6. YUAN J, ZHU S, KAI X, et al. On the construction of quantum constacyclic codes[J]. Designs Codes and Cryptography, 2017, 85(1): 179-190. doi: 10. 1007/s10623-016 -0296-2. LIU Y, LI R, L L, et al. A class of constacyclic BCH codes and new quantum codes[J]. Quantum Information Processing, 2017, 16(3): 66. doi: 10.1007/s11128-017-1533-y. XU G, LI R, and GUO L. New optimal asymmetric quantum codes constructed from constacyclic codes[J]. International Journal of Modern Physics B, 2017, 31(5): 1750030. doi: 10.1142/S0217979217500308. KRISHNA A and SARWATE D V. Pseudocyclic maximum- distance-separable codes[J]. IEEE Transactions on Information Theory, 1990, 36(4): 880-884. doi: 10.1109/ 18.53751. -
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