1,257 research outputs found
Linear Size Optimal q-ary Constant-Weight Codes and Constant-Composition Codes
An optimal constant-composition or constant-weight code of weight has
linear size if and only if its distance is at least . When , the determination of the exact size of such a constant-composition or
constant-weight code is trivial, but the case of has been solved
previously only for binary and ternary constant-composition and constant-weight
codes, and for some sporadic instances.
This paper provides a construction for quasicyclic optimal
constant-composition and constant-weight codes of weight and distance
based on a new generalization of difference triangle sets. As a result,
the sizes of optimal constant-composition codes and optimal constant-weight
codes of weight and distance are determined for all such codes of
sufficiently large lengths. This solves an open problem of Etzion.
The sizes of optimal constant-composition codes of weight and distance
are also determined for all , except in two cases.Comment: 12 page
Group Divisible Codes and Their Application in the Construction of Optimal Constant-Composition Codes of Weight Three
The concept of group divisible codes, a generalization of group divisible
designs with constant block size, is introduced in this paper. This new class
of codes is shown to be useful in recursive constructions for constant-weight
and constant-composition codes. Large classes of group divisible codes are
constructed which enabled the determination of the sizes of optimal
constant-composition codes of weight three (and specified distance), leaving
only four cases undetermined. Previously, the sizes of constant-composition
codes of weight three were known only for those of sufficiently large length.Comment: 13 pages, 1 figure, 4 table
Optimal Memoryless Encoding for Low Power Off-Chip Data Buses
Off-chip buses account for a significant portion of the total system power
consumed in embedded systems. Bus encoding schemes have been proposed to
minimize power dissipation, but none has been demonstrated to be optimal with
respect to any measure. In this paper, we give the first provably optimal and
explicit (polynomial-time constructible) families of memoryless codes for
minimizing bit transitions in off-chip buses. Our results imply that having
access to a clock does not make a memoryless encoding scheme that minimizes bit
transitions more powerful.Comment: Proceedings of the 2006 IEEE/ACM international Conference on
Computer-Aided Design (San Jose, California, November 05 - 09, 2006). ICCAD
'06. ACM, New York, NY, 369-37
Optimal Partitioned Cyclic Difference Packings for Frequency Hopping and Code Synchronization
Optimal partitioned cyclic difference packings (PCDPs) are shown to give rise
to optimal frequency-hopping sequences and optimal comma-free codes. New
constructions for PCDPs, based on almost difference sets and cyclic difference
matrices, are given. These produce new infinite families of optimal PCDPs (and
hence optimal frequency-hopping sequences and optimal comma-free codes). The
existence problem for optimal PCDPs in , with base blocks
of size three, is also solved for all .Comment: to appear in IEEE Transactions on Information Theor
The PBD-Closure of Constant-Composition Codes
We show an interesting PBD-closure result for the set of lengths of
constant-composition codes whose distance and size meet certain conditions. A
consequence of this PBD-closure result is that the size of optimal
constant-composition codes can be determined for infinite families of parameter
sets from just a single example of an optimal code. As an application, the size
of several infinite families of optimal constant-composition codes are derived.
In particular, the problem of determining the size of optimal
constant-composition codes having distance four and weight three is solved for
all lengths sufficiently large. This problem was previously unresolved for odd
lengths, except for lengths seven and eleven.Comment: 8 page
The fine intersection problem for Steiner triple systems
The intersection of two Steiner triple systems (X,A) and (X,B) is the set A
intersect B. The fine intersection problem for Steiner triple systems is to
determine for each v, the set I(v), consisting of all possible pairs (m,n) such
that there exist two Steiner triple systems of order v whose intersection has n
blocks over m points. We show that for v = 1 or 3 (mod 6), |I(v)| = Omega(v^3),
where previous results only imply that |I(v)| = Omega(v^2).Comment: 9 page
A fast algorithm for the constrained multiple sequence alignment problem
Given n strings S1, S2, ..., Sn, and a pattern string P, the constrained multiple sequence alignment (CMSA) problem is to find an optimal multiple alignment of S1, S2, ..., Sn such that the alignment contains P, i.e. in the alignment matrix there exists a sequence of columns each entirely composed of symbol P[k] for every k, where P[k] is the kth symbol in P, 1 ≤ k ≤ |P|, and in the sequence, a column containing P[i] appears before the column containing P[j] for all i,j, i < j. The problem is motivated from the problem of comparing multiple sequences that share a common structure, or sequence pattern. There are O(2ns1s2...snr)-time dynamic programming algorithms for the problem, where s1,s2, ...,sn and r are, respectively, the lengths of the input strings and the pattern string. Feasibility of these algorithms in practice is limited when the number of sequences is large, or the sequences are long because of the impractically long time required by these algorithms. We present a new algorithm with worst-case time complexity also O(2ns1s2...snr), but the algorithm avoids redundant computations in existing dynamic programming solutions. Experiments on both randomly generated strings and real data show that this algorithm is much faster than the existing algorithms. We present an analysis that explains the speed-up obtained in our experiments by our algorithm over the naive dynamic programming algorithm for constrained multiple sequence alignment of protein sequences. The speed-up is more significant when pattern is long, or n is large. For example in the case of constrained pairwise sequence alignment (the CMSA problem with n=2) when the pattern is sufficiently long for strings S1 and S2, the asymptotic time complexity is observed to be O(s1s2) instead of O(s1s2r). Main ideas in our algorithm can also be used in other constrained sequence alignment problems
On Extremal k-Graphs Without Repeated Copies of 2-Intersecting Edges
The problem of determining extremal hypergraphs containing at most r
isomorphic copies of some element of a given hypergraph family was first
studied by Boros et al. in 2001. There are not many hypergraph families for
which exact results are known concerning the size of the corresponding extremal
hypergraphs, except for those equivalent to the classical Turan numbers. In
this paper, we determine the size of extremal k-uniform hypergraphs containing
at most one pair of 2-intersecting edges for k in {3,4}. We give a complete
solution when k=3 and an almost complete solution (with eleven exceptions) when
k=4.Comment: 17 pages, 5 figure
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