New q-ary quantum MDS codes of length strictly larger than q+1

被引：0
|
作者：
Kircali, Mustafa [1 ]
Ozbudak, Ferruh [1 ,2 ]
机构：
[1] Middle East Tech Univ, Inst Appl Math, TR-06800 Ankara, Turkiye
[2] Sabanci Univ, Fac Engn & Nat Sci, TR-34956 Istanbul, Turkiye
来源：
QUANTUM INFORMATION PROCESSING | 2024年 / 23卷 / 12期
关键词：
Quantum MDS codes; Truncated code; Reed-Solomon code; Hermitian self-orthogonal code; CONSTACYCLIC CODES; CONSTRUCTION;
D O I：
10.1007/s11128-024-04598-1
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Quantum information and quantum computation have become a hot topic in recent decades. Quantum error-correcting codes are useful and have many applications in quantum computations and quantum communications. We construct a new class of quantum Maximum Distance Separable (MDS) codes. Our construction is based on a recent result of Ball and Vilar (IEEE Trans Inf Theory 68:3796-3805, 2022). We study a large class of explicit polynomials and obtain their required arithmetical properties which imply construction of new q-ary quantum MDS codes of length strictly larger than q+1, when q is odd.
引用
收藏
页数：13
相关论文
共 50 条
  • [1] CONSTRUCTIONS OF q-ARY ENTANGLEMENT-ASSISTED QUANTUM MDS CODES WITH MINIMUM DISTANCE GREATER THAN q+1
    Fan, Jihao
    Chen, Hanwu
    Xu, Juan
    QUANTUM INFORMATION & COMPUTATION, 2016, 16 (5-6) : 423 - 434
  • [2] New q-ary quantum MDS codes with distances bigger than q/2
    He, Xianmang
    Xu, Liqing
    Chen, Hao
    QUANTUM INFORMATION PROCESSING, 2016, 15 (07) : 2745 - 2758
  • [3] The Maximal Length of q-ary MDS Elliptic Codes Is Close to q/2
    Han, Dongchun
    Ren, Yuan
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2023, 2024 (11) : 9036 - 9043
  • [4] MDS constacyclic codes of length q+1 over GF(q)
    Wang, Xiaoqiang
    Ding, Cunsheng
    Liu, Hongwei
    Zheng, Dabin
    CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2024, 16 (01): : 21 - 48
  • [5] Classification of q-Ary Perfect Quantum Codes
    Li, Zhuo
    Xing, Lijuan
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2013, 59 (01) : 631 - 634
  • [6] ON (Q,1)-SUBNORMAL Q-ARY COVERING CODES
    HONKALA, I
    DISCRETE APPLIED MATHEMATICS, 1994, 52 (03) : 213 - 221
  • [7] An Asymptotic Formula in q for the Number of [n, k] q-Ary MDS Codes
    Kaipa, Krishna V.
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2014, 60 (11) : 7047 - 7057
  • [8] The Subfield Codes of Some [q+1, 2, q] MDS Codes
    Heng, Ziling
    Ding, Cunsheng
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2022, 68 (06) : 3643 - 3656
  • [9] CYCLIC AND PSEUDO-CYCLIC MDS CODES OF LENGTH Q+1
    DAHL, C
    PEDERSEN, JP
    JOURNAL OF COMBINATORIAL THEORY SERIES A, 1992, 59 (01) : 130 - 133
  • [10] On the Finite Length Scaling of q-Ary Polar Codes
    Goldin, Dina
    Burshtein, David
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2018, 64 (11) : 7153 - 7170
12345