scholarly journals Binary (k, k)-Designs

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1883
Author(s):  
Todorka Alexandrova ◽  
Peter Boyvalenkov ◽  
Angel Dimitrov
Keyword(s):  
Linear Programming ◽  
Orthogonal Arrays ◽  
General Linear ◽  
Combinatorial Interpretation ◽  
Linear Programming Bound ◽  
Universal Bound ◽  
Special Case

We introduce and investigate binary (k,k)-designs, a special case of T-designs. Our combinatorial interpretation relates (k,k)-designs to the binary orthogonal arrays. We derive a general linear programming bound and propose as a consequence a universal bound on the minimum possible cardinality of (k,k)-designs for fixed k and n. Designs which attain our bound are investigated.

Association Schemes for Ordered Orthogonal Arrays and (T, M, S)-Nets

1999 ◽  
Vol 51 (2) ◽  
pp. 326-346 ◽  
Author(s):  
W. J. Martin ◽  
D. R. Stinson
Keyword(s):  
Linear Programming ◽  
Association Scheme ◽  
Type Theorem ◽  
Orthogonal Arrays ◽  
Association Schemes ◽  
Theoretic Approach ◽  
Linear Programming Bound ◽  
Ordered Orthogonal Arrays

AbstractIn an earlier paper [10], we studied a generalized Rao bound for ordered orthogonal arrays and (T, M, S)-nets. In this paper, we extend this to a coding-theoretic approach to ordered orthogonal arrays. Using a certain association scheme, we prove a MacWilliams-type theorem for linear ordered orthogonal arrays and linear ordered codes as well as a linear programming bound for the general case. We include some tables which compare this bound against two previously known bounds for ordered orthogonal arrays. Finally we show that, for even strength, the LP bound is always at least as strong as the generalized Rao bound.

Sharpening the linear programming bound for linear Lee codes

2015 ◽  
Vol 51 (6) ◽  
pp. 492-494 ◽  
Author(s):  
H. Astola ◽  
I. Tabus
Keyword(s):  
Linear Programming ◽  
Linear Programming Bound

scholarly journals On the linear programming bound for linear Lee codes

SpringerPlus ◽  
2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Helena Astola ◽  
Ioan Tabus
Keyword(s):  
Linear Programming ◽  
Linear Programming Bound

Deconvolution with the ℓ1 norm

Geophysics ◽  
1979 ◽  
Vol 44 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Howard L. Taylor ◽  
Stephen C. Banks ◽  
John F. McCoy
Keyword(s):  
Linear Programming ◽  
Spike Train ◽  
Initial Approximation ◽  
Spike Trains ◽  
General Linear ◽  
Programming System ◽  
Sample Rate ◽  
Weighting Procedures

Given a wavelet w and a noisy trace t + s * w + n, an approximation ŝ of the spike train s can be obtained using the [Formula: see text] norm. This extraction has the advantage of preserving isolated spikes in s. On some types of data the spike train ŝ can represent s as a sparse series of spikes, which may be sampled at a rate higher than the sample rate of the data trace t. The extracted spike train ŝ may be qualitatively much different than those commonly extracted using the [Formula: see text] norm. The [Formula: see text] norm can also be used to extract a wavelet ŵ from a trace t when a spike train s is known. This wavelet extraction can be constrained to give a smooth wavelet which integrates to zero and goes to zero at the ends. Given a trace t and an initial approximation for either s or w, it is possible to alternately extract spike trains and wavelets to improve the representation of trace t. Although special algorithms have been developed to solve [Formula: see text] problems, all of the calculations can be performed using a general linear programming system. Proper weighting procedures allow these methods to be used on ungained data.

scholarly journals Applying Quantum Optimization Algorithms for Linear Programming

2017 ◽  
Author(s):  
Mert Side ◽  
Volkan Erol
Keyword(s):  
Resource Allocation ◽  
Linear Programming ◽  
Production Scheduling ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Computers ◽  
Quantum Optimization ◽  
Special Case

Quantum computers are machines that are designed to use quantum mechanics in order to improve upon classical computers by running quantum algorithms. One of the main applications of quantum computing is solving optimization problems. For addressing optimization problems we can use linear programming. Linear programming is a method to obtain the best possible outcome in a special case of mathematical programming. Application areas of this problem consist of resource allocation, production scheduling, parameter estimation, etc. In our study, we looked at the duality of resource allocation problems. First, we chose a real world optimization problem and looked at its solution with linear programming. Then, we restudied this problem with a quantum algorithm in order to understand whether if there is a speedup of the solution. The improvement in computation is analysed and some interesting results are reported.

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