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1.
In this paper, we consider a set of lines of with the properties that (1) every plane contains 0, 1 or q + 1 elements of , (2) every solid contains no more than q
2 + q + 1 and no less than q + 1 elements of , and (3) every point of is on q + 1 members of , and we show that, whenever (4) q ≠ 2 (respectively, q = 2) and the lines of through some point are contained in a solid (respectively, a plane), then is necessarily the set of lines of a regularly embedded split Cayley generalized hexagon in , with q even. We present examples of such sets not satisfying (4) based on a Singer cycle in , for all q.
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2.
Antonio Cossidente 《Designs, Codes and Cryptography》2009,51(2):123-129
In the geometric setting of commuting orthogonal and unitary polarities we construct an infinite family of complete (q + 1)2–spans of the Hermitian surface , q odd. A construction of an infinite family of minimal blocking sets of , q odd, admitting PSL
2(q), is also provided.
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3.
Maria Cristeta Cuaresma Michael Giudici Cheryl E. Praeger 《Designs, Codes and Cryptography》2008,46(3):303-327
For a graph Γ, subgroups , and an edge partition of Γ, the pair is a (G, M)-homogeneous factorisation if M is vertex-transitive on Γ and fixes setwise each part of , while G permutes the parts of transitively. A classification is given of all homogeneous factorisations of finite Johnson graphs. There are three infinite
families and nine sporadic examples.
This paper forms part of an ARC Discovery grant of the last two authors. The second author holds an Australian Research Council
Australian Research Fellowship. 相似文献
4.
Frédéric A. B. Edoukou 《Designs, Codes and Cryptography》2009,50(1):135-146
We study the functional codes of second order on a non-degenerate Hermitian variety as defined by G. Lachaud. We provide the best possible bounds for the number of points of quadratic sections of . We list the first five weights, describe the corresponding codewords and compute their number. The paper ends with two
conjectures. The first is about minimum distance of the functional codes of order h on a non-singular Hermitian variety . The second is about distribution of the codewords of first five weights of the functional codes of second order on a non-singular
Hermitian variety .
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5.
It has been known for a long time that the Deligne–Lusztig curves associated to the algebraic groups of type and defined over the finite field all have the maximum number of -rational points allowed by the Weil “explicit formulas”, and that these curves are -maximal curves over infinitely many algebraic extensions of . Serre showed that an -rational curve which is -covered by an -maximal curve is also -maximal. This has posed the problem of the existence of -maximal curves other than the Deligne–Lusztig curves and their -subcovers, see for instance Garcia (On curves with many rational points over finite fields. In: Finite Fields with Applications
to Coding Theory, Cryptography and Related Areas, pp. 152–163. Springer, Berlin, 2002) and Garcia and Stichtenoth (A maximal
curve which is not a Galois subcover of the Hermitan curve. Bull. Braz. Math. Soc. (N.S.) 37, 139–152, 2006). In this paper, a positive answer to this problem is obtained. For every q = n
3 with n = p
r
> 2, p ≥ 2 prime, we give a simple, explicit construction of an -maximal curve that is not -covered by any -maximal Deligne–Lusztig curve. Furthermore, the -automorphism group Aut has size n
3(n
3 + 1)(n
2 − 1)(n
2 − n + 1). Interestingly, has a very large -automorphism group with respect to its genus .
Research supported by the Italian Ministry MURST, Strutture geometriche, combinatoria e loro applicazioni, PRIN 2006–2007. 相似文献
6.
Mario Petrich 《Annali di Matematica Pura ed Applicata》2008,187(1):119-136
We construct a family of completely regular semigroups with the property that each completely regular semigroup S with a finite number of -classes in each -class is non-cryptic if and only if S contains an isomorphic image of a member of . Each member F of is an ideal extension of a Rees matrix semigroup J by a cyclic group B with a zero adjoined and the identity of B is the identity of F. Here with I and Λ finite, G is given by generators and relations, and P is given explicitly. Within completely regular semigroups, the cryptic property is equivalent to where is the natural partial order and a
if and only if a
2 = ab = ba. Hence the above result can be formulated in terms of and .
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7.
We prove that every [n, k, d]
q
code with q ≥ 4, k ≥ 3, whose weights are congruent to 0, −1 or −2 modulo q and is extendable unless its diversity is for odd q, where .
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8.
Let (V, g) be a Riemannian manifold and let be the isometric immersion operator which, to a map , associates the induced metric on V, where denotes the Euclidean scalar product in . By Nash–Gromov implicit function theorem is infinitesimally invertible over the space of free maps. In this paper we study non-free isometric immersions . We show that the operator (where denotes the space of C
∞- smooth quadratic forms on ) is infinitesimally invertible over a non-empty open subset of and therefore is an open map in the respective fine topologies.
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9.
Maria Bras-Amorós 《Designs, Codes and Cryptography》2007,43(2-3):137-145
One-point codes are those algebraic-geometry codes for which the associated divisor is a non-negative multiple of a single
point. Evaluation codes were defined in order to give an algebraic generalization of both one-point algebraic-geometry codes
and Reed–Muller codes. Given an -algebra A, an order function on A and given a surjective -morphism of algebras , the ith evaluation code with respect to is defined as the code . In this work it is shown that under a certain hypothesis on the -algebra A, not only any evaluation code is a one-point code, but any sequence of evaluation codes is a sequence of one-point codes.
This hypothesis on A is that its field of fractions is a function field over and that A is integrally closed. Moreover, we see that a sequence of algebraic-geometry codes G
i
with associated divisors is the sequence of evaluation codes associated to some -algebra A, some order function and some surjective morphism with if and only if it is a sequence of one-point codes.
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10.
F. E. A. Johnson 《Archiv der Mathematik》2008,90(2):123-132
A module J over a ring is said to be hyperstable when . Over a module M for which Ext we show that the projective n-stems for which is hyperstable constitute a single homotopy type.
Received: 17 November 2006 相似文献
11.
We derive the Singleton bound for poset codes and define the MDS poset codes as linear codes which attain the Singleton bound.
In this paper, we study the basic properties of MDS poset codes. First, we introduce the concept of I-perfect codes and describe the MDS poset codes in terms of I-perfect codes. Next, we study the weight distribution of an MDS poset code and show that the weight distribution of an MDS
poset code is completely determined. Finally, we prove the duality theorem which states that a linear code C is an MDS -code if and only if is an MDS -code, where is the dual code of C and is the dual poset of
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12.
Raúl E. Curto Lawrence A. Fialkow H. Michael Möller 《Integral Equations and Operator Theory》2008,60(2):177-200
For a degree 2n real d-dimensional multisequence to have a representing measure μ, it is necessary for the associated moment matrix to be positive semidefinite and for the algebraic variety associated to β, , to satisfy rank card as well as the following consistency condition: if a polynomial vanishes on , then . We prove that for the extremal case , positivity of and consistency are sufficient for the existence of a (unique, rank -atomic) representing measure. We also show that in the preceding result, consistency cannot always be replaced by recursiveness
of .
The first-named author’s research was partially supported by NSF Research Grants DMS-0099357 and DMS-0400741. The second-named
author’s research was partially supported by NSF Research Grant DMS-0201430 and DMS-0457138. 相似文献
13.
Yu. I. Lyubich 《Designs, Codes and Cryptography》2009,51(1):21-31
It is shown that among all tight designs in , where is or , or (quaternions), only 5-designs in (Lyubich, Shatalora Geom Dedicata 86: 169–178, 2001) have irrational angle set. This is the only case of equal ranks of the
first and the last irreducible idempotent in the corresponding Bose-Mesner algebra.
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14.
For a smooth curve C it is known that a very ample line bundle on C is normally generated if Cliff() < Cliff(C) and there exist extremal line bundles (:non-normally generated very ample line bundle with Cliff() = Cliff(C)) with . However it has been unknown whether there exists an extremal line bundle with . In this paper, we prove that for any positive integers (g, c) with g = 2c + 5 and (mod 2) there exists a smooth curve of genus g and Clifford index c carrying an extremal line bundle with . In fact, a smooth quadric hypersurface section C of a general projective K3 surface always has an extremal line bundle with . More generally, if C has a line bundle computing the Clifford index c of C with , then C has such an extremal line bundle .
For all authors, this work was supported by Korea Research Foundation Grant funded by Korea Government (MOEHRD, Basic Reasearch
Promotion Fund)(KRF-2005-070-C00005). 相似文献
15.
Sven Kosub 《Mathematics in Computer Science》2008,1(3):487-505
A complete classification of the computational complexity of the fixed-point existence problem for Boolean dynamical systems,
i.e., finite discrete dynamical systems over the domain {0, 1}, is presented. For function classes and graph classes , an ()-system is a Boolean dynamical system such that all local transition functions lie in and the underlying graph lies in . Let be a class of Boolean functions which is closed under composition and let be a class of graphs which is closed under taking minors. The following dichotomy theorems are shown: (1) If contains the self-dual functions and contains the planar graphs, then the fixed-point existence problem for ()-systems with local transition function given by truth-tables is NP-complete; otherwise, it is decidable in polynomial time.
(2) If contains the self-dual functions and contains the graphs having vertex covers of size one, then the fixed-point existence problem for ()-systems with local transition function given by formulas or circuits is NP-complete; otherwise, it is decidable in polynomial
time.
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16.
Let X be a Banach space. We give characterizations of when is a u-ideal in for every Banach space Y in terms of nets of finite rank operators approximating weakly compact operators. Similar characterizations are given for
the cases when is a u-ideal in for every Banach space Y, when is a u-ideal in for every Banach space Y, and when is a u-ideal in for every Banach space Y. 相似文献
17.
Let G be a connected graph. For at distance 2, we define , and , if then . G is quasi-claw-free if it satisfies , and G is P
3-dominated() if it satisfies , for every pair (x, y) of vertices at distance 2. Certainly contains as a subclass. In this paper, we prove that the circumference of a 2-connected P
3-dominated graph G on n vertices is at least min or , moreover if then G is hamiltonian or , where is a class of 2-connected nonhamiltonian graphs. 相似文献
18.
Let Γ6 be the elliptic curve of degree 6 in PG(5, q) arising from a non-singular cubic curve of PG(2, q) via the canonical Veronese embedding
(1) If Γ6 (equivalently ) has n
GF(q)-rational points, then the associated near-MDS code has length n and dimension 6. In this paper, the case q = 5 is investigated. For q = 5, the maximum number of GF(q)-rational points of an elliptic curve is known to be equal to ten. We show that for an elliptic curve with ten GF(5)-rational points, the associated near-MDS code can be extended by adding two more points of PG(5, 5). In this way we obtain six non-isomorphic [12, 6]5 codes. The automorphism group of is also considered.
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19.
Valentina S. Harizanov Carl G. JockuschJr. Julia F. Knight 《Archive for Mathematical Logic》2009,48(1):39-53
We study the complexity of infinite chains and antichains in computable partial orderings. We show that there is a computable
partial ordering which has an infinite chain but none that is or , and also obtain the analogous result for antichains. On the other hand, we show that every computable partial ordering
which has an infinite chain must have an infinite chain that is the difference of two sets. Our main result is that there is a computably axiomatizable theory K of partial orderings such that K has a computable model with arbitrarily long finite chains but no computable model with an infinite chain. We also prove
the corresponding result for antichains. Finally, we prove that if a computable partial ordering has the feature that for every , there is an infinite chain or antichain that is relative to , then we have uniform dichotomy: either for all copies of , there is an infinite chain that is relative to , or for all copies of , there is an infinite antichain that is relative to . 相似文献
20.
Haïkel Skhiri 《Integral Equations and Operator Theory》2008,62(1):137-148
Let be the algebra of all bounded linear operators on a complex Banach space X and γ(T) be the reduced minimum modulus of operator . In this work, we prove that if , is a surjective linear map such that is an invertible operator, then , for every , if and only if, either there exist two bijective isometries and such that for every , or there exist two bijective isometries and such that for every . This generalizes for a Banach space the Mbekhta’s theorem [12].
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