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An intersection problem for codes

P. Frankl
1990 Discrete Mathematics  
The problem of determining max IAl for A being (t" . . . , t,)-intersecting is considered.  ...  . , &)-intersecting if for any two members ci, b E A and any 1 s i < s there are at least r, positions j, where both a' and b have entry i, that is, a, = b, = i.  ...  . , a,} be an alphabet of size s and consider X = A", the set of all words (xi, . . . , x,) of length n over A, i.e. Xi E A for all i. A set C c X is called a code.  ... 
doi:10.1016/0012-365x(90)90369-s fatcat:k6j6yru4kvhy7i2wd4zjklzyxi

Intersection of Isomorphic Linear Codes

Eli Bar-Yahalom, Tuvi Etzion
1997 Journal of combinatorial theory. Series A  
The intersection problem is to determine which integers in this range are attainable for a given code C.  ...  As a consequence we give a complete solution to the intersection problem for most of the interesting linear codes, e.g. cyclic codes, Reed Muller codes, and most MDS codes.  ...  ACKNOWLEDGMENTS The authors thank Alexander Vardy and an anonymous referee for their constructive comments.  ... 
doi:10.1006/jcta.1997.2805 fatcat:iej7x7jsy5e5plck67i262sqki

SNIFF: A Search Engine for Java Using Free-Form Queries [chapter]

Shaunak Chatterjee, Sudeep Juvekar, Koushik Sen
2009 Lecture Notes in Computer Science  
We use the documentation of the library methods to add plain English meaning to an otherwise undocumented user code. The annotated user code is then indexed for the purpose of free-form query search.  ...  Recent research efforts have tried to address this problem by automating the generation of code snippets from user queries.  ...  Our current results for free-form queries are already better than several existing code search engines.  ... 
doi:10.1007/978-3-642-00593-0_26 fatcat:vgtodxu6nffxtduhhsqdklf5ga

Covering arrays and intersecting codes

N. J. A. Sloane
1993 Journal of combinatorial designs (Print)  
One of the principal constructions makes use of intersecting codes (linear codes with the property that any two nonzero codewords meet).  ...  This article studies the properties of 3-covering arrays and intersecting codes, and gives a table of the best 3-covering arrays presently known.  ...  an [NI N2, K1 K z , D1 Dz] intersecting code [14].  ... 
doi:10.1002/jcd.3180010106 fatcat:fzaevcbqsrbzfp6gvgcxswfzpm

Kikuchi approximation method for joint decoding of LDPC codes and partial-response channels

P. Pakzad, V. Anantharam
2006 IEEE Transactions on Communications  
In this letter, we apply the Kikuchi approximation method to the problem of joint decoding of a low-density parity-check code and a partial-response channel.  ...  The Kikuchi method is, in general, more powerful than the conventional loopy belief propagation (BP) algorithm, and can produce better approximations to an underlying inference problem.  ...  Fig. 1 . 1 Block diagram of the serial concatenation of an LDPC code and a PR channel. Fig. 2 . 2 Junction-graph model for joint BP decoding of the LDPC/PR problem.  ... 
doi:10.1109/tcomm.2006.877944 fatcat:krlotuvwanfkxnmhisludzaaqi

On the intersection of additive perfect codes [article]

Authors J. Rifà, F. Solov'eva, M. Villanueva
2006 arXiv   pre-print
The intersection problem for additive (extended and non-extended) perfect codes, i.e. which are the possibilities for the number of codewords in the intersection of two additive codes C1 and C2 of the  ...  For all these codes the abelian group structure of the intersection is characterized.  ...  We investigate the intersection problem for such codes and the abelian group structure for their intersection codes.  ... 
arXiv:cs/0612015v1 fatcat:h3etmdhndfdmnoqflra4b43rle

On generic erasure correcting sets and related problems [article]

Rudolf Ahlswede, Harout Aydinian
2011 arXiv   pre-print
We observe that these two conceps are closely related to so called s--wise intersecting codes, an area, in which G(r,s) has been studied primarily with respect to ratewise performance.  ...  Finally, we observed that hypergraph covering can be used for both problems to derive good upper bounds.  ...  Acknowledgement The second author would like to thank anonymous referees for their comments.  ... 
arXiv:1108.1161v1 fatcat:re5ecv64tzb7tbftqlg2qs57r4

An information theoretic view of network management

T. Ho, M. Medard, R. Koetter
2003 IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428)  
We present an information theoretic framework for network management for non-ergodic link failures.  ...  We give bounds on network management requirements for various network connection problems in terms of basic parameters such as the number of source processes and the number of links in a minimum sourcereceiver  ...  An interior codé µ is called valid for the network connection problem if there exists some for which´ µ is a valid code for the problem.  ... 
doi:10.1109/infcom.2003.1208981 dblp:conf/infocom/HoMK03 fatcat:qkh4r7xxyvahblyodtb2esicnm

An Information-Theoretic View of Network Management

T. Ho, M. Medard, R. Koetter
2005 IEEE Transactions on Information Theory  
We present an information theoretic framework for network management for non-ergodic link failures.  ...  We give bounds on network management requirements for various network connection problems in terms of basic parameters such as the number of source processes and the number of links in a minimum sourcereceiver  ...  An interior codé µ is called valid for the network connection problem if there exists some for which´ µ is a valid code for the problem.  ... 
doi:10.1109/tit.2005.844062 fatcat:6onr6mlq4ffkzkaplcc4locyxu

On Generic Erasure Correcting Sets and Related Problems

Rudolf Ahlswede, Harout Aydinian
2012 IEEE Transactions on Information Theory  
We observe that these two conceps are closely related to intersecting codes, an area, in which G(r, s) has been studied primarily with respect to ratewise performance. We derive connections.  ...  Finally, we observed that hypergraph covering can be used for both problems to derive good upper bounds.  ...  Some known results about intersecting codes We present some known results on intersecting codes which can be used for our problems.  ... 
doi:10.1109/tit.2011.2173729 fatcat:inmvzc4xrrhnhmjnk52ycluiai

Equidistant Linear Codes in Projective Spaces [article]

Pranab Basu
2021 arXiv   pre-print
Thus we establish that the problem of finding equidistant linear codes of maximum size in ℙ_q(n) with constant distance 2d is equivalent to the problem of finding the largest d-intersecting family of subspaces  ...  Our discovery proves that there exist equidistant linear codes of size more than 2^n for every prime power q > 2.  ...  Arvind Ayyer for their valuable inputs.  ... 
arXiv:2107.10820v1 fatcat:gmckoqtfmbgv5fnlyubkxvghru

An Efficient and Robust Ray-Box Intersection Algorithm

Amy Williams, Steve Barrus, R. Keith Morley, Peter Shirley
2005 Journal of Graphics Tools  
Sample source code is available online.  ...  The computational bottleneck in a ray tracer using bounding volume hierarchies is often the ray intersection routine with axis-aligned bounding boxes.  ...  Brian Smits' advocacy for BVH intersection methods and care with IEEE properties gave us the initial impetus for this work.  ... 
doi:10.1080/2151237x.2005.10129188 fatcat:ggzcxw3moba6xmjkl76y6ihfha

An efficient and robust ray-box intersection algorithm

Amy Williams, Steve Barrus, R. Keith Morley, Peter Shirley
2005 ACM SIGGRAPH 2005 Courses on - SIGGRAPH '05  
Sample source code is available online.  ...  The computational bottleneck in a ray tracer using bounding volume hierarchies is often the ray intersection routine with axis-aligned bounding boxes.  ...  Brian Smits' advocacy for BVH intersection methods and care with IEEE properties gave us the initial impetus for this work.  ... 
doi:10.1145/1198555.1198748 dblp:conf/siggraph/WilliamsBMS05 fatcat:asq7h4f67bg3bkx7454gbscjzy

Traffic State Recognition of Intersection Based on Image Model and PCA Hashing

Li-li Zhang, Li Wang, Qi Zhao
2020 Journal of Advanced Transportation  
Then, the traffic state recognition problem at the intersection is translated into an image searching problem with tags. The image searching is realized by the hashing algorithm.  ...  To this end, we construct an image model for intersections and implement image feature extraction in a way that is different from traditional image processing.  ...  Section IV describes the transformation of the traffic state recognition problem at the intersection into an image search problem and designs an image search based on PCA (Principal Components Analysis  ... 
doi:10.1155/2020/3828395 fatcat:x6egso3zhnan5ovlc2gehiosue

Extremal 1-codes in distance-regular graphs of diameter 3

Aleksandar Jurišić, Janoš Vidali
2012 Designs, Codes and Cryptography  
Introduction Infinite families Problems Bibliography Families with codes An open case We have much information about the structure. No costruction or proof of nonexistence is known.  ...  Introduction Infinite families Problems Bibliography Distance-regular graphs Codes in distance-regular graphs Triple intersection numbers Krein parameters In the Bose-Mesner algebra M, the following  ...  For any u ∈ V Γ with u ∼ v and ∂(u , w ) = 2 we have u v w 3 3 3 = 1. If Γ has intersection array (1), then there is no solution and Γ does not exist.  ... 
doi:10.1007/s10623-012-9651-0 fatcat:bhbfhpvvp5cmnjv23ss7si55y4
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