611 research outputs found
On the constructions of ZpZp2-linear generalized Hadamard codes
Altres ajuts: acord transformatiu CRUE-CSICThe ZZ-additive codes are subgroups of Z ×Z , and can be seen as linear codes over Z when α=0, Z-additive codes when α=0, or ZZ-additive codes when p=2. A ZZ-linear generalized Hadamard (GH) code is a GH code over Z which is the Gray map image of a ZZ-additive code. In this paper, we generalize some known results for ZZ-linear GH codes with p=2 to any p≥3 prime when α≠0. First, we give a recursive construction of ZZ-additive GH codes of type (α,α;t,t) with t,t≥1. We also present many different recursive constructions of ZZ-additive GH codes having the same type, and show that we obtain permutation equivalent codes after applying the Gray map. Finally, according to some computational results, we see that, unlike Z-linear GH codes, when p≥3 prime, the Z-linear GH codes are not included in the family of ZZ-linear GH codes with α≠0. Indeed, we observe that the constructed codes are not equivalent to the Z-linear GH codes for any s≥2
Integral point sets over finite fields
We consider point sets in the affine plane where each
Euclidean distance of two points is an element of . These sets
are called integral point sets and were originally defined in -dimensional
Euclidean spaces . We determine their maximal cardinality
. For arbitrary commutative rings
instead of or for further restrictions as no three points on a
line or no four points on a circle we give partial results. Additionally we
study the geometric structure of the examples with maximum cardinality.Comment: 22 pages, 4 figure
Second p descents on elliptic curves
Let p be a prime and let C be a genus one curve over a number field k
representing an element of order dividing p in the Shafarevich-Tate group of
its Jacobian. We describe an algorithm which computes the set of D in the
Shafarevich-Tate group such that pD = C and obtains explicit models for these D
as curves in projective space. This leads to a practical algorithm for
performing 9-descents on elliptic curves over the rationals.Comment: 45 page
On permanents of Sylvester Hadamard matrices
It is well-known that the evaluation of the permanent of an arbitrary
-matrix is a formidable problem. Ryser's formula is one of the fastest
known general algorithms for computing permanents. In this paper, Ryser's
formula has been rewritten for the special case of Sylvester Hadamard matrices
by using their cocyclic construction. The rewritten formula presents an
important reduction in the number of sets of distinct rows of the matrix to
be considered. However, the algorithm needs a preprocessing part which remains
time-consuming in general
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
Near-complete external difference families
We introduce and explore near-complete external difference families, a partitioning of the nonidentity elements of a group so that each nonidentity element is expressible as a difference of elements from distinct subsets a fixed number of times. We show that the existence of such an object implies the existence of a near-resolvable design. We provide examples and general constructions of these objects, some of which lead to new parameter families of near-resolvable designs on a non-prime-power number of points. Our constructions employ cyclotomy, partial difference sets, and Galois rings.PostprintPeer reviewe
Derived category of toric varieties with Picard number three
We construct a full, strongly exceptional collection of line bundles on the
variety X that is the blow up of the projectivization of the vector bundle
O_{P^{n-1}}\oplus O_{P^{n-1}}(b) along a linear space of dimension n-2, where b
is a non-negative integer
Propene oligomerization over steam dealuminated and boron and phospherous modified ZSM-5
Bibliography: pages 203-210.ZSM-5 was modified with boron and phosphorus compounds in an attempt to improve the selectivity of the catalyst with respect to the linearity of the liquid product of propene oligomerization. Boron was incorporated into the zeolite framework by inclusion in the synthesis gel. Boralite catalysts made in this way and containing very low Al contents had only weak acidity as was evident from only one, low temperature NH3 desorption peak at ca. 190 °C. These catalysts showed poor propene oligomerization activity as a result of the weak acidity arising from the weak B(OH)Si site and reduced catalyst free volume. The latter was ascribed to occluded B₂O₃ species. Activity of these catalysts was proportional to Al, rather than B content. No appreciable selectivity changes were observed for any of these catalysts. In an attempt to enhance the acidity and hence the activity of the boralite catalysts, mild fluorination treatments were carried out. A boralite catalyst containing 550 ppm Al and 1.2 wt% boron was treated with mild HF at room temperature. The activity of the catalyst was significantly reduced. The activity of the catalyst was essentially restored to its former level upon subsequent NH₄F treatment. The catalyst then contained 120 ppm Al and 0.8 wt% boron. Although some activity enhancement was achieved through mild fluorination, the catalyst utilization values (CUV) remained an order of magnitude lower than the CUV of unmodified ZSM-5. Catalytic activity remained proportional to trace Al content
- …