New construction of error-correcting pooling designs from singular linear spaces over finite fields

2020 ◽  
Author(s):  
Gang Wang ◽  
You Gao
Keyword(s):  
Finite Fields ◽  
Pooling Designs ◽  
Linear Spaces ◽  
New Construction ◽  
Singular Linear Spaces

scholarly journals Construction of random pooling designs based on singular linear space over finite fields

2021 ◽  
Vol 7 (3) ◽  
pp. 4376-4385
Author(s):  
Xuemei Liu ◽  
◽  
Yazhuo Yu
Keyword(s):  
Linear Space ◽  
Finite Fields ◽  
Pooling Designs ◽  
Linear Spaces ◽  
Disjunct Matrix ◽  
Short Time ◽  
Singular Linear Spaces

<abstract><p>Faced with a large number of samples to be tested, if there are requiring to be tested one by one and complete in a short time, it is difficult to save time and save costs at the same time. The random pooling designs can deal with it to some degree. In this paper, a family of random pooling designs based on the singular linear spaces and related counting theorems are constructed. Furtherly, based on it we construct an $ \alpha $-$ almost\ d^e $-disjunct matrix and an $ \alpha $-$ almost\ (d, r, z] $-disjunct matrix, and all the parameters and properties of these random pooling designs are given. At last, by comparing to Li's construction, we find that our design is better under certain condition.</p></abstract>

scholarly journals Some New Constructions of Authentication Codes with Arbitration and Multi-Receiver from Singular Symplectic Geometry

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
You Gao ◽  
Huafeng Yu
Keyword(s):  
Probability Distribution ◽  
Finite Fields ◽  
Symplectic Geometry ◽  
Authentication Codes ◽  
Uniform Probability ◽  
Different Types ◽  
Uniform Probability Distribution ◽  
New Construction

A new construction of authentication codes with arbitration and multireceiver from singular symplectic geometry over finite fields is given. The parameters are computed. Assuming that the encoding rules are chosen according to a uniform probability distribution, the probabilities of success for different types of deception are also computed.

Quasi-regular semilattices in singular linear spaces

2016 ◽  
Vol 08 (01) ◽  
pp. 1650005
Author(s):  
Baohuan Zhang ◽  
Yujun Liu ◽  
Zengti Li
Keyword(s):  
Finite Field ◽  
Linear Space ◽  
Fixed Integer ◽  
Linear Spaces ◽  
Partially Ordered ◽  
Type Formula ◽  
Singular Linear Spaces

Let [Formula: see text] denote the [Formula: see text]-dimensional singular linear space over a finite field [Formula: see text]. For a fixed integer [Formula: see text], denote by [Formula: see text] the set of all subspaces of type [Formula: see text], where [Formula: see text]. Partially ordered by ordinary inclusion, one family of quasi-regular semilattices is obtained. Moreover, we compute its all parameters.

scholarly journals Classical access structures of ramp secret sharing based on quantum stabilizer codes

2019 ◽  
Vol 19 (1) ◽  
Author(s):  
Ryutaroh Matsumoto
Keyword(s):  
Finite Fields ◽  
Secret Sharing ◽  
Sufficient Conditions ◽  
Secret Sharing Schemes ◽  
Sufficient Condition ◽  
Linear Spaces ◽  
Stabilizer Codes ◽  
Access Structures ◽  
Necessary And Sufficient ◽  
Quantum Stabilizer Codes

AbstractIn this paper, we consider to use the quantum stabilizer codes as secret sharing schemes for classical secrets. We give necessary and sufficient conditions for qualified and forbidden sets in terms of quantum stabilizers. Then, we give a Gilbert–Varshamov-type sufficient condition for existence of secret sharing schemes with given parameters, and by using that sufficient condition, we show that roughly 19% of participants can be made forbidden independently of the size of classical secret, in particular when an n-bit classical secret is shared among n participants having 1-qubit share each. We also consider how much information is obtained by an intermediate set and express that amount of information in terms of quantum stabilizers. All the results are stated in terms of linear spaces over finite fields associated with the quantum stabilizers.

scholarly journals A NEW CONSTRUCTION FOR POOLING DESIGNS

2011 ◽  
Vol 85 (1) ◽  
pp. 121-127
Author(s):  
FENGLIANG JIN ◽  
HOUCHUN ZHOU ◽  
JUAN XU
Keyword(s):  
Library Screening ◽  
Pooling Design ◽  
Pooling Designs ◽  
Disjunct Matrix ◽  
Helpful Tool ◽  
Dna Library ◽  
New Family ◽  
New Construction ◽  
Dna Library Screening ◽  
Disjunct Matrices

AbstractPooling designs are a very helpful tool for reducing the number of tests for DNA library screening. A disjunct matrix is usually used to represent the pooling design. In this paper, we construct a new family of disjunct matrices and prove that it has a good row to column ratio and error-tolerant property.

Class dimension of association schemes in singular linear spaces

2017 ◽  
Vol 09 (01) ◽  
pp. 1750005
Author(s):  
Haixia Guo ◽  
You Gao
Keyword(s):  
Association Scheme ◽  
Upper Bounds ◽  
Association Schemes ◽  
Resolving Set ◽  
Linear Spaces ◽  
Set Of Points ◽  
Special Case ◽  
Singular Linear Spaces

A resolving set for an association scheme [Formula: see text] is a set of points [Formula: see text] such that, for all [Formula: see text], the ordered list of relations [Formula: see text] uniquely determines [Formula: see text], where [Formula: see text] denotes the relation [Formula: see text] containing the pair [Formula: see text] in [Formula: see text]. In this paper, we determine upper bounds on class dimension for a family of association schemes in singular linear spaces, and construct their resolving sets for a special case.

scholarly journals t-Singular Linear Spaces

2016 ◽  
Vol 23 (02) ◽  
pp. 227-238
Author(s):  
Jun Guo ◽  
Fenggao Li ◽  
Kaishun Wang
Keyword(s):  
Linear Groups ◽  
Linear Spaces ◽  
Singular Linear Spaces

As a generalization of singular linear spaces, we introduce the concept of t-singular linear spaces, make some anzahl formulas of subspaces, and determine the suborbits of t-singular linear groups.

scholarly journals A New Construction of Multisender Authentication Codes from Polynomials over Finite Fields

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Xiuli Wang
Keyword(s):  
Finite Fields ◽  
Authentication Codes ◽  
Authentication Code ◽  
Polynomials Over Finite Fields ◽  
New Construction

Multisender authentication codes allow a group of senders to construct an authenticated message for a receiver such that the receiver can verify the authenticity of the received message. In this paper, we construct one multisender authentication code from polynomials over finite fields. Some parameters and the probabilities of deceptions of this code are also computed.

A new construction of approximately SIC-POVMs derived from Jacobi sums over finite fields

2021 ◽  
Vol 20 (2) ◽  
Author(s):  
Gaojun Luo ◽  
Xiwang Cao ◽  
Dandan Wang ◽  
Qiuyan Wang
Keyword(s):  
Finite Fields ◽  
Jacobi Sums ◽  
New Construction
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