排序方式: 共有11条查询结果,搜索用时 31 毫秒
1.
A 3‐phase Barker array is a matrix of third roots of unity for which all out‐of‐phase aperiodic autocorrelations have magnitude 0 or 1. The only known truly two‐dimensional 3‐phase Barker arrays have size 2 × 2 or 3 × 3. We use a mixture of combinatorial arguments and algebraic number theory to establish severe restrictions on the size of a 3‐phase Barker array when at least one of its dimensions is divisible by 3. In particular, there exists a double‐exponentially growing arithmetic function T such that no 3‐phase Barker array of size with exists for all . For example, , , and . When both dimensions are divisible by 3, the existence problem is settled completely: if a 3‐phase Barker array of size exists, then . 相似文献
2.
We give a combinatorial construction of a one-parameter and a two-parameter family of complete caps in finite projective spaces
over GF(2). As an application of our construction we find, for each α ε[1.89,2], a sequence of complete caps in PG(n,2) whose sizes grow roughly as α
n
. We also discuss the relevance of our caps to the problem of finding the least dependent caps of a given cardinality in a
given dimension.
*Research partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).
An erratum to this article is available at . 相似文献
3.
A Roman dominating function on a graph G = (V(G), E(G)) is a labelling ${f : V(G)\rightarrow \{0,1,2\}}$ satisfying the condition that every vertex with label 0 has at least a neighbour with label 2. The Roman domination number γ R (G) of G is the minimum of ${\sum_{v \in V(G)}{f(v)}}$ over all such functions. The Roman bondage number b R (G) of G is the minimum cardinality of all sets ${E\subseteq E(G)}$ for which γ R (G \ E) > γ R (G). Recently, it was proved that for every planar graph P, b R (P) ≤ Δ(P) + 6, where Δ(P) is the maximum degree of P. We show that the Roman bondage number of every planar graph does not exceed 15 and construct infinitely many planar graphs with Roman bondage number equal to 7. 相似文献
4.
Petteri Kaski Mahdad Khatirinejad Patric R. J. Östergård 《Designs, Codes and Cryptography》2012,62(3):323-330
Higman asked which block graphs of Steiner triple systems of order v satisfy the 4-vertex condition and left the cases v = 9, 13, 25 unsettled.We give a complete answer to this question by showing that the affine plane of order 3 and the binary
projective spaces are the only such systems. The major part of the proof is to show that no block graph of a Steiner triple
system of order 25 satisfies the 4-vertex condition. 相似文献
5.
On Weyl-Heisenberg orbits of equiangular lines 总被引:1,自引:0,他引:1
Mahdad Khatirinejad 《Journal of Algebraic Combinatorics》2008,28(3):333-349
An element
is called fiducial if {gz:g∈G} is a set of lines with only one angle between each pair, where G
≅ℤ
d
×ℤ
d
is the one-dimensional finite Weyl-Heisenberg group modulo its centre. We give a new characterization of fiducial vectors.
Using this characterization, we show that the existence of almost flat fiducial vectors implies the existence of certain cyclic
difference sets. We also prove that the construction of fiducial vectors in prime dimensions 7 and 19 due to Appleby (J. Math.
Phys. 46(5):052107, 2005) does not generalize to other prime dimensions (except for possibly a set with density zero). Finally, we use our new characterization
to construct fiducial vectors in dimension 7 and 19 whose coordinates are real.
Research supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). 相似文献
6.
Mode locking a 1550 nm semiconductor disk laser by using a GaInNAs saturable absorber 总被引:1,自引:0,他引:1
Lindberg H Sadeghi M Westlund M Wang S Larsson A Strassner M Marcinkevicius S 《Optics letters》2005,30(20):2793-2795
Passive mode locking of an optically pumped, InP-based, 1550 nm semiconductor disk laser by using a GaInNAs saturable absorber mirror is demonstrated. To reduce material heating and enable high-power operation, a 50 microm thick diamond heat spreader is bonded to the surface of the gain chip. The laser operates at a repetition frequency of 2.97 GHz and emits near-transform-limited 3.2 ps pulses with an average output power of 120 mW. 相似文献
7.
8.
We give new recursive constructions of complete caps in PG(n,2). We approach the problem of constructing caps with low dependency via the doubling construction and comparison to lower
bounds. We report results of the exhaustive classification (up to projective equivalence) of all caps in PG(n,2) for n≤ 6.
Research partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) 相似文献
9.
A triple cyclically contains the ordered pairs , , , and no others. A Mendelsohn triple system of order v, or , is a set V together with a collection of ordered triples of distinct elements from V, such that and each ordered pair with is cyclically contained in exactly λ ordered triples. By means of a computer search, we classify all Mendelsohn triple systems of order 13 with ; there are 6 855 400 653 equivalence classes of such systems. 相似文献
10.