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On a linear code from a configuration of affine lines [article]

Ken-ichi Sugiyama
2007 arXiv   pre-print
We will show how to obtain a linear code from a configuration of affine lines in general position and a suitable set of rational points.  ...  We will also explain a new decoding algorithm based on the configuration, which seems to be quite effective.  ...  Acknowledgements The author is partially supported by the Grand-in-Aid for Scientific Research (C) No.18540203, the Ministry of Eduvation, Culture, Sports, Science and Technology, Japan.  ... 
arXiv:0708.2784v1 fatcat:jacqfdvkbjav5jcat5jvp3avkm

Incidence Structures From the Blown–Up Plane and LDPC Codes

Alain Couvreur
2011 IEEE Transactions on Information Theory  
Such a feature is absent from random LDPC codes and is in general interesting for the efficiency of iterative decoding. The performance of some codes under iterative decoding is tested.  ...  They arise from sets of conics in the affine plane blown-up at its rational points. The LDPC codes given by these incidence matrices are studied.  ...  Acknowledgements The author expresses a deep gratitude to Daniel Augot and Gilles Zémor for many inspiring discussions. Computations and simulations have been made using Magma.  ... 
doi:10.1109/tit.2011.2146490 fatcat:ynvlpqns2jcr5dpgqceh5fobsm

Sparse Representation with Geometric Configuration Constraint for Line Segment Matching [chapter]

Qing Wang, Tingwang Chen
2012 Lecture Notes in Computer Science  
We present a novel line segment matching method based on sparse representation with geometric configuration constraint.  ...  Features of all line segments are trained into a dictionary using sparse coding. Lines with the same similarity may fall together in the high dimensional feature space.  ...  Suppose we have two pairs of matched lines Conclusions In this paper, we have proposed a novel method for line matching over multiple views based on sparse coding with geometric configuration constraint  ... 
doi:10.1007/978-3-642-31919-8_64 fatcat:fl545ns7wbcsrhhdpvfrp7br2a

Toric Codes and Finite Geometries [article]

John B. Little
2017 arXiv   pre-print
We show how the theory of affine geometries over the ring Z/〈 q - 1〉 can be used to understand the properties of toric and generalized toric codes over F_q.  ...  This point of view should be useful both as a way to visualize properties of these codes and as a guide to heuristic searches for good codes constructed in this fashion.  ...  The lines in the affine plane G have a familiar-looking parametric form and the points on a line are in one-to-one correspondence with the elements of R because it is required that (u, v) ∈ B.  ... 
arXiv:1504.07494v2 fatcat:uhuugt5rzra7pgf42ehag47otq

Page 6139 of Mathematical Reviews Vol. , Issue 93k [page]

1993 Mathematical Reviews  
A line of this space is either a line or a qg-cap of the original space. The family of quadrics hence forms an incidence structure isomorphic to the affine space itself. J. W. P.  ...  Ferenc Wettl (H-BUDT) 93k:51013 51E21 Bruen, A. A. (3-WON); Fisher, J. Chris (3-RGN) An observation on certain point-line configurations in classical planes.  ... 

The dual minimum distance of arbitrary-dimensional algebraic–geometric codes

Alain Couvreur
2012 Journal of Algebra  
In this article, the minimum distance of the dual C^ of a functional code C on an arbitrary dimensional variety X over a finite field _q is studied.  ...  The approach consists in finding minimal configurations of points on X which are not in "general position".  ...  Acknowledgements The author expresses a deep gratitude to Marc Perret and Daniel Augot for their relevant comments about this article.  ... 
doi:10.1016/j.jalgebra.2011.09.030 fatcat:giogksi3fnfi7npd5d5sjzbuk4

L-convex-concave body in ${\boldmath{$\mathbb{R}P^3$}}$ contains a line

A. Khovanskii, D. Novikov
2003 Geometric and Functional Analysis  
We define a class of L-convex-concave subsets of RP 3 , where L is a projective line in RP 3 . These are sets whose sections by any plane containing L are convex and concavely depend on this plane.  ...  We prove a version of Arnold's conjecture for these sets, namely we prove that each such set contains a line. Conjecture 1 (Main Conjecture).  ...  A configuration corresponding to a Chebyshev line cannot be coded by a code containing 1+, 2+, 3+ and 4+. Proof.  ... 
doi:10.1007/s00039-003-0440-9 fatcat:3a73nifsxbeh3hhg5i7e6uruua

Rectification, and Segmentation of Coplanar Repeated Patterns

James Pritts, Ondrej Chum, Jiri Matas
2014 2014 IEEE Conference on Computer Vision and Pattern Recognition  
Rectification to within a similarity of the scene plane is achieved from one rotated repeat, or to within a similarity with a scale ambiguity along the axis of symmetry from one reflected repeat.  ...  A stratum of constraints is derived that gives the necessary configuration of repeats for each successive level of rectification.  ...  For two pairs of line segments, there are 3 + 2 = 5 unknowns and four linear equations, yielding a one-dimensional linear space of solutions.  ... 
doi:10.1109/cvpr.2014.380 dblp:conf/cvpr/PrittsCM14 fatcat:z5yidqdyi5aspclmngjbxujap4

Convex-concave body in RP^3 contains a line [article]

A. Khovanskii, D. Novikov
2002 arXiv   pre-print
We define a class of L-convex-concave subsets of RP^3, where L is a projective line in RP^3. These are sets whose sections by any plane containing L are convex and concavely depend on this plane.  ...  We prove a version of Arnold hypothesis for these sets, namely we prove that each such set contains a line.  ...  Configuration corresponding to a Chebyshev line cannot be coded by a code containing 1+, 2+, 3+ and 4+.Proof.  ... 
arXiv:math/0203200v1 fatcat:nvoriwlqijesjesct7av7pwbey

Page 4754 of Mathematical Reviews Vol. , Issue 88i [page]

1988 Mathematical Reviews  
The linear codes, considered in the context of (S, 2), arise from subsets of S that are of even or odd type, a subset of S being of even [resp. odd] type if every line intersects it in an even [resp. odd  ...  Hence f maps any additively closed subset . of P(S) onto a linear code f (7) =~, and the minimum weight of this code is the minimum cardinality of the nonempty subsets of 7.  ... 

Plane polynomials and Hamiltonian vector fields determined by their singular points [article]

John A. Arredondo, Jesús Muciño-Raymundo
2022 arXiv   pre-print
A dichotomy appears for the values of δ (d); depending on a certain parity the space of essentially determined polynomials is an open or closed Zariski set.  ...  The quotient space of essentially determined polynomials of degree three up to the action of the affine group Aff(𝕂^2) determines a singular surface over 𝕂.  ...  For degree d ě 3, a particular family of configurations is the grids of pd ´1q 2 points from the intersection of two families of d parallel lines in K 2 , see Definition 8.  ... 
arXiv:2206.05569v1 fatcat:k2wzwsewhrc3diuxkrenfvfedi

General Video Coding Technology in Responses to the Joint Call for Proposals on Video Compression with Capability beyond HEVC

Benjamin Bross, Kenneth Andersson, Max Blaser, Virginie Drugeon, Seung-Hwan Kim, Jani Lainema, Jingya Li, Shan Liu, Jens-Rainer Ohm, Gary J. Sullivan, Ruoyang Yu
2019 IEEE transactions on circuits and systems for video technology (Print)  
higher coding efficiency, including development of a Joint Exploration Model (JEM) algorithm and a corresponding software implementation.  ...  This article provides an overview of technology that was proposed in the responses to the CfP, with a focus on techniques that were not already explored in the JEM context.  ...  Illustration of predicting one line of samples using a traditional prediction angle from the left reference (deviating less than 45 degrees from the horizontal direction) and with a wide-angle alternative  ... 
doi:10.1109/tcsvt.2019.2949619 fatcat:i4oimql6sbhhrafdb275djpe64

A White-Box Speck Implementation using Self-Equivalence Encodings (Full Version) [article]

Joachim Vandersmissen, Adrián Ranea, Bart Preneel
2022 IACR Cryptology ePrint Archive  
While this result shows that the linear and affine self-equivalences of speck are insecure, we hope that this negative result will spur additional research in higher-degree self-equivalence encodings for  ...  We propose an algebraic attack to fully recover the master key and external encodings from a white-box speck implementation, with limited effort required.  ...  Adrián Ranea is supported by a PhD Fellowship from the Research Foundation -Flanders (FWO). The authors would like to thank the anonymous reviewers for their comments and suggestions.  ... 
dblp:journals/iacr/VandersmissenRP22 fatcat:gkntrwtjcbfgjamp3ngpkofwra

Trifocal motion modeling for object-based video compression and manipulation

Zhaohui Sun, A.M. Tekalp
1998 IEEE transactions on circuits and systems for video technology (Print)  
Trifocal transfer requires a trifocal tensor that is computed by matching image features across three views and a dense correspondence between two of the three views.  ...  transform on several video sequences.  ...  across two views using a linear system of equations.  ... 
doi:10.1109/76.718512 fatcat:edktgcwm6rdbrba4ljjzpt6vbi


2014 Forum of Mathematics, Sigma  
We show that the presence of a sufficiently large number of approximately collinear triples in a set of points in${\mathbb{C}}^d$implies that the points arecloseto a low dimensional affine subspace.  ...  Thus lines are replaced by narrow tubes, and more generally affine subspaces are replaced by their small neighborhood.  ...  Saraf and A. Wigderson were partially supported by NSF grant CCF-0832797.  ... 
doi:10.1017/fms.2014.1 fatcat:ja35abqgbrapbinxilkojuc4mu
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