scholarly journals New quantum MDS codes

2014 ◽  
Vol 12 (04) ◽  
pp. 1450019 ◽  
Author(s):  
Guanghui Zhang ◽  
Bocong Chen
Keyword(s):  
Positive Integer ◽  
Prime Power ◽  
Maximum Distance ◽  
Mds Codes ◽  
Maximum Distance Separable ◽  
Minimum Distances ◽  
Quantum Mds Codes

In this paper, we construct two classes of new quantum maximum-distance-separable (MDS) codes with parameters [Formula: see text], where q is an odd prime power with q ≡ 3 (mod 4) and [Formula: see text]; [[8(q - 1), 8(q - 1) - 2d + 2, d]]q, where q is an odd prime power with the form q = 8t - 1 (t is an even positive integer) and [Formula: see text]. Comparing the parameters with all known quantum MDS codes, the quantum MDS codes exhibited here have minimum distances bigger than the ones available in the literature.

scholarly journals ON OPTIMAL QUANTUM CODES

2004 ◽  
Vol 02 (01) ◽  
pp. 55-64 ◽  
Author(s):  
MARKUS GRASSL ◽  
THOMAS BETH ◽  
MARTIN RÖTTELER
Keyword(s):  
Minimum Distance ◽  
Prime Power ◽  
Quantum Systems ◽  
Error Correcting Codes ◽  
Mds Codes ◽  
Quantum Codes ◽  
Maximum Distance Separable ◽  
Shortened Codes ◽  
Quantum Error ◽  
Quantum Mds Codes

We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary prime power. It is shown that codes with parameters 〚n, n - 2d + 2, d〛q exist for all 3≤n≤q and 1≤d≤n/2+1. We also present quantum MDS codes with parameters 〚q2, q2-2d+2, d〛q for 1≤d≤q which additionally give rise to shortened codes 〚q2-s, q2-2d+2-s, d〛q for some s.

New entanglement-assisted quantum MDS codes

2021 ◽  
pp. 2150016
Author(s):  
Binbin Pang ◽  
Shixin Zhu ◽  
Liqi Wang
Keyword(s):  
Coding Theory ◽  
Minimum Distance ◽  
Linear Codes ◽  
Error Correcting Codes ◽  
Mds Codes ◽  
Maximum Distance Separable ◽  
Number Formula ◽  
Minimum Distances ◽  
Quantum Error ◽  
Quantum Mds Codes

Entanglement-assisted quantum error-correcting codes (EAQECCs) can be obtained from arbitrary classical linear codes based on the entanglement-assisted stabilizer formalism, which greatly promoted the development of quantum coding theory. In this paper, we construct several families of [Formula: see text]-ary entanglement-assisted quantum maximum-distance-separable (EAQMDS) codes of lengths [Formula: see text] with flexible parameters as to the minimum distance [Formula: see text] and the number [Formula: see text] of maximally entangled states. Most of the obtained EAQMDS codes have larger minimum distances than the codes available in the literature.

Construction of new quantum MDS codes derived from constacyclic codes

2017 ◽  
Vol 15 (01) ◽  
pp. 1750008 ◽  
Author(s):  
Divya Taneja ◽  
Manish Gupta ◽  
Rajesh Narula ◽  
Jaskaran Bhullar
Keyword(s):  
Minimum Distance ◽  
Maximum Distance ◽  
Mds Codes ◽  
Constacyclic Codes ◽  
Maximum Distance Separable ◽  
Work Done ◽  
Quantum Mds Codes

Obtaining quantum maximum distance separable (MDS) codes from dual containing classical constacyclic codes using Hermitian construction have paved a path to undertake the challenges related to such constructions. Using the same technique, some new parameters of quantum MDS codes have been constructed here. One set of parameters obtained in this paper has achieved much larger distance than work done earlier. The remaining constructed parameters of quantum MDS codes have large minimum distance and were not explored yet.

MDS Constacyclic Codes of Prime Power Lengths Over Finite Fields and Construction of Quantum MDS Codes

2020 ◽  
Vol 59 (10) ◽  
pp. 3043-3078
Author(s):  
Hai Q. Dinh ◽  
Ramy Taki ElDin ◽  
Bac T. Nguyen ◽  
Roengchai Tansuchat
Keyword(s):  
Finite Fields ◽  
Prime Power ◽  
Mds Codes ◽  
Constacyclic Codes ◽  
Quantum Mds Codes

scholarly journals Direct Construction of Optimal Rotational-XOR Diffusion Primitives

2017 ◽  
pp. 169-187 ◽  
Author(s):  
Zhiyuan Guo ◽  
Renzhang Liu ◽  
Si Gao ◽  
Wenling Wu ◽  
Dongdai Lin
Keyword(s):  
Diffusion Layer ◽  
Hash Function ◽  
Block Cipher ◽  
Exhaustive Search ◽  
Maximum Distance ◽  
Mds Codes ◽  
Cyclic Structure ◽  
Core Component ◽  
Direct Construction ◽  
Maximum Distance Separable

As a core component of SPN block cipher and hash function, diffusion layer is mainly introduced by matrices built from maximum distance separable (MDS) codes. Up to now, most MDS constructions require to perform an equivalent or even exhaustive search. In this paper, we study the cyclic structure of rotational-XOR diffusion layer, a commonly used diffusion primitive over (

New LCD MDS codes constructed from generalized Reed–Solomon codes

2019 ◽  
Vol 18 (08) ◽  
pp. 1950150 ◽  
Author(s):  
Xueying Shi ◽  
Qin Yue ◽  
Shudi Yang
Keyword(s):  
Finite Field ◽  
Coding Theory ◽  
Theory And Practice ◽  
Maximum Distance ◽  
Mds Codes ◽  
Reed Solomon Codes ◽  
Maximum Distance Separable ◽  
Maximum Distance Separable Codes ◽  
Invertible Matrices

Maximum distance separable codes with complementary duals (LCD MDS codes) are very important in coding theory and practice, and have attracted a lot of attention. In this paper, we focus on LCD MDS codes constructed from generalized Reed–Solomon (GRS) codes over a finite field with odd characteristic. We detail two constructions of new LCD MDS codes, using invertible matrices and the roots of three classes of polynomials, respectively.

New quantum codes from Hermitian dual-containing codes

2019 ◽  
Vol 17 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Xiusheng Liu ◽  
Long Yu ◽  
Hualu Liu
Keyword(s):  
Linear Code ◽  
Maximum Distance ◽  
Mds Codes ◽  
Quantum Codes ◽  
Generator Matrix ◽  
Maximum Distance Separable ◽  
New Criterion

Hermitian dual-containing codes play an important role in the constructing quantum codes. In this paper, we present a new criterion of Hermitian dual-containing code based on the rank of generator matrix for a linear code. Then, using the criterion, we construct a class of new quantum maximum-distance-separable (MDS) codes and some new quantum codes.

scholarly journals PURE ASYMMETRIC QUANTUM MDS CODES FROM CSS CONSTRUCTION: A COMPLETE CHARACTERIZATION

2013 ◽  
Vol 11 (03) ◽  
pp. 1350027 ◽  
Author(s):  
MARTIANUS FREDERIC EZERMAN ◽  
SOMPHONG JITMAN ◽  
HAN MAO KIAH ◽  
SAN LING
Keyword(s):  
Error Correcting Codes ◽  
Complete Characterization ◽  
Maximum Distance ◽  
Mds Codes ◽  
Singleton Bound ◽  
Asymmetric Quantum ◽  
Maximum Distance Separable ◽  
Mds Conjecture ◽  
Css Construction ◽  
Quantum Error

Using the Calderbank–Shor–Steane (CSS) construction, pure q-ary asymmetric quantum error-correcting codes attaining the quantum Singleton bound are constructed. Such codes are called pure CSS asymmetric quantum maximum distance separable (AQMDS) codes. Assuming the validity of the classical maximum distance separable (MDS) Conjecture, pure CSS AQMDS codes of all possible parameters are accounted for.

Symbol-triple distance of repeated-root constacyclic codes of prime power lengths

2019 ◽  
Vol 19 (11) ◽  
pp. 2050209 ◽  
Author(s):  
Hai Q Dinh ◽  
Sampurna Satpati ◽  
Abhay Kumar Singh ◽  
Woraphon Yamaka
Keyword(s):  
Prime Power ◽  
Nonzero Element ◽  
Maximum Distance ◽  
Constacyclic Codes ◽  
Chain Ring ◽  
Maximum Distance Separable ◽  
Positive Integers

Let [Formula: see text] be an odd prime, [Formula: see text] and [Formula: see text] be positive integers and [Formula: see text] be a nonzero element of [Formula: see text]. The [Formula: see text]-constacyclic codes of length [Formula: see text] over [Formula: see text] are linearly ordered under set theoretic inclusion as ideals of the chain ring [Formula: see text]. Using this structure, the symbol-triple distances of all such [Formula: see text]-constacyclic codes are established in this paper. All maximum distance separable symbol-triple constacyclic codes of length [Formula: see text] are also determined as an application.

Maximum Distance Separable Hankel Rhotrices over Finite Fields

2018 ◽  
Vol 43 (1-4) ◽  
pp. 13-45
Author(s):  
Prof. P. L. Sharma ◽  
◽  
Mr. Arun Kumar ◽  
Mrs. Shalini Gupta ◽  
◽  
...  
Keyword(s):  
Finite Fields ◽  
Maximum Distance ◽  
Maximum Distance Separable
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