Quantum error-correcting codes from projective Reed-Muller codes and their hull variation problem

被引：0
作者：
Ruano, Diego [1 ]
San-Jose, Rodrigo [1 ]
机构：
[1] Univ Valladolid, IMUVA Math Res Inst, Valladolid 47011, Spain
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2025年
关键词：
Projective Reed-Muller codes; quantum codes; subfield subcodes; Hermitian product; hull;
D O I：
10.1142/S0219498825410099
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Long quantum codes using projective Reed-Muller codes are constructed. Projective Reed-Muller codes are evaluation codes obtained by evaluating homogeneous polynomials at the projective space. We obtain asymmetric and symmetric quantum codes by using the CSS construction and the Hermitian construction, respectively. We provide entanglement-assisted quantum error-correcting codes from projective Reed-Muller codes with flexible amounts of entanglement by considering equivalent codes. Moreover, we also construct quantum codes from subfield subcodes of projective Reed-Muller codes.
引用
收藏
页数：15
相关论文
共 29 条
  • [1] Anderson S. E., Camps-Moreno E., Lopez H. H., Matthews G. L., Ruano D., Soprunov I., Relative hulls and quantum codes, IEEE Trans. Inform. Theory, 70, 5, pp. 3190-3201, (2024)
  • [2] Ball S., Some constructions of quantum MDS codes, Des. Codes Cryptogr, 89, 5, pp. 811-821, (2021)
  • [3] Bierbrauer J., Edel Y., Quantum twisted codes, J. Combin. Des, 8, 3, pp. 174-188, (2000)
  • [4] Bosma W., Cannon J., Playoust C., The Magma algebra system. I. The user language, J. Symbolic Comput, 24, 3-4, pp. 235-265, (1997)
  • [5] Brun T., Devetak I., Hsieh M.-H., Correcting quantum errors with entanglement, Science, 314, 5798, pp. 436-439, (2006)
  • [6] Calderbank A. R., Shor P. W., Good quantum error-correcting codes exist, Phys. Rev. A, 54, pp. 1098-1105, (1996)
  • [7] Chen H., On the hull-variation problem of equivalent linear codes, IEEE Trans. Inform. Theory, 69, 5, pp. 2911-2922, (2023)
  • [8] Delsarte P., Goethals J.-M., MacWilliams F. J., On generalized Reed-Muller codes and their relatives, Inf. Control, 16, pp. 403-442, (1970)
  • [9] Feng K., Ma Z., A finite Gilbert-Varshamov bound for pure stabilizer quantum codes, IEEE Trans. Inform. Theory, 50, 12, pp. 3323-3325, (2004)
  • [10] Galindo C., Hernando F., Matsumoto R., Ruano D., Entanglement-assisted quantum error-correcting codes over arbitrary finite fields, Quantum Inf. Process, 18, 4, (2019)
123