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

页数：13

共 50 条

[31] EFFICIENT Q-ARY IMMUTABLE CODES
CAPOCELLI, RM
GARGANO, L
VACCARO, U
DISCRETE APPLIED MATHEMATICS, 1991, 33 (1-3) : 25 - 41
[32] A New Class of Q-Ary Codes for the McEliece Cryptosystem
Freudenberger, Juergen
Thiers, Johann-Philipp
CRYPTOGRAPHY, 2021, 5 (01)
[33] On the construction of q-ary equidistant codes
Bogdanova, G. T.
Zinoviev, V. A.
Todorov, T. J.
PROBLEMS OF INFORMATION TRANSMISSION, 2007, 43 (04) : 280 - 302
[34] On the construction of q-ary equidistant codes
G. T. Bogdanova
V. A. Zinoviev
T. J. Todorov
Problems of Information Transmission, 2007, 43 : 280 - 302
[35] GRAPH THEORETIC Q-ARY CODES
BOBROW, LS
HAKIMI, SL
IEEE TRANSACTIONS ON INFORMATION THEORY, 1971, 17 (02) : 215 - +
[36] The q-Ary Antiprimitive BCH Codes
Zhu, Hongwei
Shi, Minjia
Wang, Xiaoqiang
Helleseth, Tor
IEEE TRANSACTIONS ON INFORMATION THEORY, 2022, 68 (03) : 1683 - 1695
[37] On normal and subnormal q-ary codes
Lobstein, Antoine C., 1600, (35):
[38] Ranks of q-ary 1-perfect codes
Phelps, KT
Villanueva, M
DESIGNS CODES AND CRYPTOGRAPHY, 2002, 27 (1-2) : 139 - 144
[39] Ranks of q-Ary 1-Perfect Codes
Kevin T. Phelps
Mercè Villanueva
Designs, Codes and Cryptography, 2002, 27 : 139 - 144
[40] q-Ary Chain-Containing Quantum Synchronizable Codes
Xie, Yixuan
Yang, Lei
Yuan, Jinhong
IEEE COMMUNICATIONS LETTERS, 2016, 20 (03) : 414 - 417

← 1 2 3 4 5 →