Representation of Subspaces and Enumerative Encoding of the Grassmannian Space (2009)
Silberstein, Natalia, Etzion, Tuvi
Codes in the Grassmannian space have found recently application in network coding. Representation of $k$-dimensional subspaces of $\F_q^n$ has generally an essential role in solving coding problems...
Sequence Folding, Lattice Tiling, and Multidimensional Coding (2009)
Folding a sequence $S$ into a multidimensional box is a well-known method which is used as a multidimensional coding technique. The operation of folding is generalized in a way that the sequence $S$...
High Dimensional Error-Correcting Codes (2009)
In this paper we construct multidimensional codes with high dimension. The codes can correct high dimensional errors which have the form of either small clusters, or confined to an area with a small...
Folding, Tiling, and Multidimensional Coding (2009)
Folding a sequence $S$ into a multidimensional box is a method that is used to construct multidimensional codes. The well known operation of folding is generalized in a way that the sequence $S$ can...
Enumerative Encoding in the Grassmannian Space (2009)
Silberstein, Natalia, Etzion, Tuvi
Codes in the Grassmannian space have found recently application in network coding. Representation of $k$-dimensional subspaces of $\F_q^n$ has generally an essential role in solving coding problems...
NEW UPPER BOUNDS ON CODES VIA ASSOCIATION SCHEMES AND LINEAR PROGRAMMING (2008)
Beniamin Mounits, Tuvi Etzion, Simon Litsyn
(Communicated by Eimear Byrne) Abstract. Let A(n, d) denote the maximum number of codewords in a binary code of length n and minimum Hamming distance d. Upper and lower bounds on A(n, d) have been a...
Blackburn, Simon R., Etzion, Tuvi, Martin, Keith M., Paterson, Maura B.
A two-dimensional grid with dots is called a \emph{configuration with distinct differences} if any two lines which connect two dots are distinct either in their length or in their slope. These...
Distinct Difference Configurations: Multihop Paths and Key Predistribution in Sensor Networks (2008)
Blackburn, Simon R., Etzion, Tuvi, Martin, Keith M., Paterson, Maura B.
A distinct difference configuration is a set of points in $\mathbb{Z}^2$ with the property that the vectors (\emph{difference vectors}) connecting any two of the points are all distinct. Many...
On row-by-row coding for 2-D constraints (2008)
Tal, Ido, Etzion, Tuvi, Roth, Ron M.
A constant-rate encoder--decoder pair is presented for a fairly large family of two-dimensional (2-D) constraints. Encoding and decoding is done in a row-by-row manner, and is sliding-block...
Error-Correcting Codes in Projective Spaces via Rank-Metric Codes and Ferrers Diagrams (2008)
Etzion, Tuvi, Silberstein, Natalia
Coding in the projective space has received recently a lot of attention due to its application in network coding. Reduced row echelon form of the linear subspaces and Ferrers diagram can play a key...
Construction of Error-Correcting Codes for Random Network Coding (2008)
Etzion, Tuvi, Silberstein, Natalia
In this work we present error-correcting codes for random network coding based on rank- metric codes, Ferrers diagrams, and puncturing. For most parameters, the constructed codes are larger than all...
Coding Theory in Projective Space (2008)
Silberstein, Natalia, Etzion, Tuvi
Projective space of order $n$ over a finite field $GF(q)$, denoted by $\mathcal{P}_{q}(n),$ is a set of all the subspaces of a vector space $GF(q)^{n}.$ The projective space is a metric space with...
Coding Theory in Projective Space (2008)
Silberstein, Natalia, Etzion, Tuvi
Projective space of order $n$ over a finite field $GF(q)$, denoted by $\mathcal{P}_{q}(n),$ is a set of all the subspaces of a vector space $GF(q)^{n}.$ The projective space is a metric space with...
Coding Theory in Projective Spaces (2008)
Abstract — Given the n-dimensional space F n q, the elements of the projective spaces are all subspaces of F n q. Recently these codes have found application in error-correction of network coding....
PROLIFIC CODES WITH THE IDENTIFIABLE PARENT PROPERTY ∗ (2008)
Simon R. Blackburn, Tuvi Etzion, Siaw-lynn Ng
Abstract. Let C be a code of length n over an alphabet of size q. A word d is a descendant of a pair of codewords x, y ∈ C if di ∈ {xi, yi} for 1 ≤ i ≤ n. A code C is an identifiable parent...
Marina Biberstein, Tuvi Etzion, Senior Member
Theorem 2.9 is not contained in Theorem 2.10. �Y � paramters in Theorems 2.6, 2.9, or 2.10.
E cient Encoding Algorithm for Third-Order Spectral-Null Codes (2008)
Vitaly Skachek, Tuvi Etzion, Ron M. Roth
An e cient algorithm is presented for encoding unconstrained information se-quences into a third-order spectral-null code of length n and redundancy 9log 2 n + O(log log n). The encoding can be...
maximum throughput is more profound. Fig. 9 shows S,,,, versus M with h as a parameter. We see that initially S,,,, increases with M (which is expected). However, as M increases beyond 1.0 h=O 1
Simon R. Blackburn, Tuvi Etzion, Douglas R. Stinson, Gregory M. Zaverucha
The paper provides an upper bound on the size of a (generalised) separating hash family, a notion introduced by Stinson, Wei and Chen. The upper bound generalises and unifies several previously known...
Error-Correction of Multidimensional Bursts (2007)
In this paper we present several constructions to generate codes for correcting a multidimensional cluster-error. The goal is to correct a cluster-error whose shape can be a box-error, a Lee sphere...
Normal and Abnormal Codes (2007)
J. K. Omura, Wi R. Bellman, S. Dreyfus, Programming Princeton, ...
[71 J.L. Massey “Error bounds for tree codes, trellis codes, and convolutional
Which Codes Have Cycle-Free Tanner Graphs? (2007)
Tuvi Etzion, Ari Trachtenberg, Alexander Vardy
If a linear block code C of length n has a Tanner graph without cycles, then maximum-likelihood soft-decision decoding of C can be achieved in time O(n^2). However, we show that cycle-free Tanner...
Simon R. Blackburn, Tuvi Etzion, Douglas R. Stinson, Gregory M. Zaverucha
The paper provides an upper bound on the size of a (generalised) separating hash family, a notion introduced by Stinson, Wei and Chen. The upper bound generalises and unifies several previously known...
Simon R. Blackburn, Tuvi Etzion, Douglas R. Stinson, Gregory M. Zaverucha
The paper provides an upper bound on the size of a (generalised) separating hash family, a notion introduced by Stinson, Wei and Chen. The upper bound generalises and unifies several previously known...
The positive capacity region of twodimensional run length constrained channels (2006)
if every run of zeros (with possible exception of the first and the last runs) has length at least � and at most �. A binary two-dimensional array satisfies a
New Upper Bounds on A(n,d) (2005)
Mounits, Beniamin, Etzion, Tuvi, Litsyn, Simon
Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and...
Configuration Distribution and Designs of Codes in the Johnson Scheme (2005)
Abstract: The main goal of this article is to present several connections between perfect codes in the Johnson scheme and designs, and provide new tools for proving Delsarte conjecture that there are...
Two-dimensional cluster-correcting codes (2005)
Abstract—We consider two-dimensional error-correcting codes capable of correcting a single arbitrary cluster of errors of size. We provide optimal P-cluster-correcting codes in several connectivity...
Optimal Tristance Anticodes in Certain Graphs (2004)
Etzion, Tuvi, Schwartz, Moshe, Vardy, Alexander
For $z_1,z_2,z_3 \in \Z^n$, the \emph{tristance} $d_3(z_1,z_2,z_3)$ is a generalization of the $L_1$-distance on $\Z^n$ to a quantity that reflects the relative dispersion of three points rather than...
Zero/Positive Capacities of Two-Dimensional Runlength Constrained Arrays (2004)
Tuvi Etzion, Kenneth G. Paterson
A binary sequence satisfies a one-dimensional (d 1 , k 1 , d 2 , k 2 ) runlength constraint if every run of zeroes has length at least d 1 and at most k 2 and every run of ones has length at least d...
Perfect constant-weight codes (2004)
Abstract—In his pioneering work from 1973, Delsarte conjectured that there are no nontrivial perfect codes in the Johnson scheme. Many attempts were made, during the years which followed, to prove...
Optimal 2-dimensional 3-dispersion lattices (2003)
Abstract. We examine 2-dimensional 3-dispersion lattice interleavers in three connectivity models: the rectangular grid with either 4 or 8 neighbors, and the hexagonal grid. We provide tight lower...
Improved upper bounds on sizes of codes (2002)
Beniamin Mounits, Tuvi Etzion, Simon Litsyn, Senior Member, Senior Member
Abstract—Let @ A denote the maximum possible number of codewords in a binary code of length and minimum Hamming distance. For large values of, the best known upper bound, for fixed, is the Johnson...
Two-dimensional interleaving schemes with repetitions: Constructions and bounds (2002)
Tuvi Etzion, Senior Member, Er Vardy
Abstract—Two-dimensional interleaving schemes with repetitions are considered. These schemes are required for the correction of two-dimensional bursts (or clusters) of errors in applications such...
Zero/positive capacities of two-dimensional runlength constrained arrays (2001)
Tuvi Etzion, Kenneth G. Paterson
Abstract—A binary sequence satisfies a one-dimensional @ I I P PA runlength constraint if every run of zeros has length at least I and at most I and every run of ones has length at least P and at...
: www.idealibrary.com on Codes and Anticodes in the Grassman Graph (2000)
Perfect codes and optimal anticodes in the Grassman graph G q(n, k) are examined. It is shown that the vertices of the Grassman graph cannot be partitioned into optimal anticodes, with a possible...
Which codes have cycle-free tanner graphs (1999)
Tuvi Etzion, Senior Member, Ari Trachtenberg, Student Member, Er Vardy, C Ci
Abstract — If a linear block code of length � has a Tanner graph without cycles, then maximum-likelihood soft-decision decoding of can be achieved in time y@ � P A. However, we show that...
Efficient encoding algorithm for third-order spectralnull codes (1998)
Vitaly Skachek, Tuvi Etzion, Ron M. Roth, Senior Member
Abstract — An efficient algorithm is presented for encoding unconstrained information sequences into a third-order spectral-null code of length � and redundancy W���P � C
Efficient Encoding Algorithm for Third-Order Spectral-Null Codes (1998)
Vitaly Skachek, Tuvi Etzion, Ron M. Roth
An efficient algorithm is presented for encoding unconstrained information sequences into a third-order spectral-null code of length n and redundancy 9 log 2 n + O(log log n). The encoding can be...
Greedy and heuristic algorithms for codes and colorings (1998)
Many of the fundamental coding problems can be represented as graph problems. These problems are often intrinsically diOEcult and unsolved even if the code length is relatively small. With the...
The depth distribution—A new characterization for linear codes (1997)
Abstract—We apply the well-known operator of sequences, the derivative h, on codewords of linear codes. The depth of a codeword ™ is the smallest integer � such that h � ™ (the derivative...
Efficient code constructions for certain two-dimensional constraints (1997)
Roman Talyansky, Tuvi Etzion, Ron M. Roth
Efficient encoding algorithms are presented for two types of constraints on two-dimensional binary arrays. The rst constraint considered is that of t-conservative arrays, where each row and each...
A method for constructing decodable de Bruijn Sequences (1996)
Chris J. Mitchell, Tuvi Etzion, Member Ieee, Member Ieee, Kenneth G. Paterson
Abstract-In this paper we present two related methods of construction for de Bruijn sequences, both based on interleaving “smaller ” de Bruijn sequences. Sequences obtained using these...
Constructions for optimal constantweight cyclically permutable codes and difference families (1995)
Abstract-A cyclically permutable code is a binary code whose codewords are cyclically distinct and have full cyclic order. An important class of these codes are the constant weight cyclically...
Perfect binary codes: constructions, properties and enumeration (1994)
Abstract-Properties of nonlinear perfect binary codes are investigated and several new constructions of perfect codes are derived from these properties. An upper bound on the cardinal-ity of the...
On the distribution of de Bruijn sequence of given complexity (1984)
E. F. Brickell, Tuvi Etzion, Abraham Lempel
[28] Y. Desmedt,*j. Vandewalle, and R. Govaerts,“A general public key cryptographic knapsack algorithm based on linear algebra, ” in
Cascading Methods for Runlength-Limited Arrays (1983)
E. F. Assmus, V. S. Pless, Tuvi Etzion
[4] J. H. Conway and N. J. A. Sloane, “A new upper bound on the minimal