Algorithms for the Solution of the Quadratic Congruence

1929 ◽  
Vol 36 (2) ◽  
pp. 83
Author(s):  
H. S. Vandiver
Keyword(s):  
Quadratic Congruence

An Improved Outsourcing Algorithm to Solve Quadratic Congruence Equations in Internet of Things

2021 ◽  
pp. 1-1
Author(s):  
Xiulan Li ◽  
Jingguo Bi ◽  
Chengliang Tian ◽  
Hanlin Zhang ◽  
Jia Yu ◽  
...  
Keyword(s):  
Internet Of Things ◽  
Quadratic Congruence ◽  
Outsourcing Algorithm

On the number of incongruent solutions to a quadratic congruence over algebraic integers

2019 ◽  
Vol 15 (01) ◽  
pp. 105-130
Author(s):  
Ramy F. Taki Eldin
Keyword(s):  
Prime Ideal ◽  
Number Field ◽  
Exponential Sums ◽  
Nonzero Ideal ◽  
Explicit Formulas ◽  
Algebraic Integers ◽  
Ideal Formula ◽  
Quadratic Congruence ◽  
Ring Of Algebraic Integers

Over the ring of algebraic integers [Formula: see text] of a number field [Formula: see text], the quadratic congruence [Formula: see text] modulo a nonzero ideal [Formula: see text] is considered. We prove explicit formulas for [Formula: see text] and [Formula: see text], the number of incongruent solutions [Formula: see text] and the number of incongruent solutions [Formula: see text] with [Formula: see text] coprime to [Formula: see text], respectively. If [Formula: see text] is contained in a prime ideal [Formula: see text] containing the rational prime [Formula: see text], it is assumed that [Formula: see text] is unramified over [Formula: see text]. Moreover, some interesting identities for exponential sums are proved.

Quadratic-Congruence Carrier-Hopping Prime Code for Multicode-Keying Optical CDMA

2007 ◽  
Author(s):  
Wing C. Kwong ◽  
Cheng-Yuan Chang ◽  
Hung-Ta Chen ◽  
Guu-Chang Yang
Keyword(s):  
Optical Cdma ◽  
Quadratic Congruence

Distribution of the roots of a quadratic congruence

1992 ◽  
Vol 62 (4) ◽  
pp. 2936-2942
Author(s):  
O. M. Fomenko
Keyword(s):  
Quadratic Congruence

On the addition of two weighted squares of units mod n

2016 ◽  
Vol 12 (07) ◽  
pp. 1783-1790 ◽  
Author(s):  
Cui-Fang Sun ◽  
Zhi Cheng
Keyword(s):  
Positive Integer ◽  
Number Of Solutions ◽  
Residue Classes ◽  
Quadratic Congruence

For any positive integer [Formula: see text], let [Formula: see text] be the ring of residue classes modulo [Formula: see text] and [Formula: see text] be the group of its units. Recently, for any [Formula: see text], Yang and Tang obtained a formula for the number of solutions of the quadratic congruence [Formula: see text] with [Formula: see text] units, nonunits and mixed pairs, respectively. In this paper, for any [Formula: see text], we give a formula for the number of representations of [Formula: see text] as the sum of two weighted squares of units modulo [Formula: see text]. We resolve a problem recently posed by Yang and Tang.

scholarly journals An Efficient Method to Reduce an MAI’s Effect in Spectral Amplitude Coding OCDMA Network

2017 ◽  
Vol 2 (6) ◽  
pp. 1
Author(s):  
Kamal Elsiddig Amaseb ◽  
Hassan Yousif Ahmed ◽  
Medien Zeghid
Keyword(s):  
Optical Communication ◽  
System Performance ◽  
Code Division Multiple Access ◽  
Multiple Access ◽  
Multiple Access Interference ◽  
Spectral Amplitude ◽  
Integer Number ◽  
Quadratic Congruence ◽  
Spectral Amplitude Coding ◽  
Code Division Multiple

Multiple access interference (MAI) in spectral-amplitude coding, optical code division multiple access (SAC-OCDMA) scheme hardly limits the system performance. This problem increases proportionally with the amount of concurrent users. In addition, phase induces intensity noise (PIIN) coming from the spontaneous emission process of light source is extra impairment leads to system drop needs to be tackled too. Towards overcome the specified problems, vector combinatorial (VC) codes which based on grouping of certain vectors is proposed. Any positive integer number can be used in both weighs and user parameters in code building procedure, these technique nominees our code to be a potential reliable applicant for future optical communication schemes. Such flexibility is an exceptional property for VC compared to SAC-OCDMA counterparts’ codes. Compared with the systems employing Hadamard, Modified Frequency Hopping (MFH), Modified Quadratic-Congruence (MQC), and Modified Double Weight (MDW), numerical results show that, the VC is effective to reduce the power of MAI and PIIN. It has been exposed that, performance can be superior significantly when VC is used.

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