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1.
A (q+1)-fold blocking set of size (q+1)(q4+q2+1) in PG(2, q4) which is not the union of q+1 disjoint Baer subplanes, is constructed 相似文献
2.
A mixed partition of PG(2n−1,q2) is a partition of the points of PG(2n−1,q2) into (n−1)-spaces and Baer subspaces of dimension 2n−1. In (Bruck and Bose, J. Algebra 1 (1964) 85) it is shown that such a mixed partition of PG(2n−1,q2) can be used to construct a (2n−1)-spread of PG(4n−1,q) and hence a translation plane of order q2n. In this paper, we provide several new examples of such mixed partitions in the case when n=2. 相似文献
3.
Joseph E. Bonin 《Advances in Applied Mathematics》1996,17(4):460-476
It is known that a geometry with rankrand no minor isomorphic to the (q+2)-point line has at most (qr−1)/(q−1) points, with strictly fewer points ifr>3 andqis not a prime power. Forqnot a prime power andr>3, we show thatqr−1−1 is an upper bound. Forqa prime power andr>3, we show that any rank-rgeometry with at leastqr−1points and no (q+2)-point-line minor is representable overGF(q). We strengthen these bounds toqr−1−(qr−2−1)/(q−1)−1 andqr−1−(qr−2−1)/(q−1) respectively whenqis odd. We give an application to unique representability and a new proof of Tutte's theorem: A matroid is binary if and only if the 4-point line is not a minor. 相似文献
4.
5.
Anuradha Sharma Gurmeet K. Bakshi V. C. Dumir Madhu Raka 《Finite Fields and Their Applications》2004,10(4):133
Let q be an odd prime power and p be an odd prime with gcd(p,q)=1. Let order of q modulo p be f,
and qf=1+pλ. Here expressions for all the primitive idempotents in the ring Rpn=GF(q)[x]/(xpn−1), for any positive integer n, are obtained in terms of cyclotomic numbers, provided p does not divide λ if n2. The dimension, generating polynomials and minimum distances of minimal cyclic codes of length pn over GF(q) are also discussed. 相似文献
6.
For the group O(p,q) we give a new construction of its minimal unitary representation via Euclidean Fourier analysis. This is an extension of the q=2 case, where the representation is the mass zero, spin zero representation realized in a Hilbert space of solutions to the wave equation. The group O(p,q) acts as the Möbius group of conformal transformations on
, and preserves a space of solutions of the ultrahyperbolic Laplace equation on
. We construct in an intrinsic and natural way a Hilbert space of solutions so that O(p,q) becomes a continuous irreducible unitary representation in this Hilbert space. We also prove that this representation is unitarily equivalent to the representation on L2(C), where C is the conical subvariety of the nilradical of a maximal parabolic subalgebra obtained by intersecting with the minimal nilpotent orbit in the Lie algebra of O(p,q). 相似文献
7.
M. A. Grechkoseeva 《Siberian Mathematical Journal》2007,48(1):73-75
We prove that the nonisomorphic simple groups B
n
(q) and C
n
(q) have different sets of element orders.
Original Russian Text Copyright ? 2007 Grechkoseeva M. A.
__________
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 1, pp. 89–92, January–February, 2007. 相似文献
8.
A square matrix over the complex field with non-negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful permutation representation of G is denoted by p(G). The minimal degree of a faithful representation of G by quasi-permutation matrices over the rational and the complex numbers are denoted by q(G) and c(G) respectively. Finally r(G) denotes the minimal degree of a faithful rational valued complex character of G. In this paper p(G), q(G), c(G) and r(G) are calculated for the groups PSU (3, q2) and SU (3, q2).AMS Subject Classification (2000): 20C15 相似文献
9.
Jianqin Zhou 《Designs, Codes and Cryptography》2011,58(3):279-296
In this paper, we first optimize the structure of the Wei–Xiao–Chen algorithm for the linear complexity of sequences over GF(q) with period N = 2p
n
, where p and q are odd primes, and q is a primitive root modulo p
2. The second, an union cost is proposed, so that an efficient algorithm for computing the k-error linear complexity of a sequence with period 2p
n
over GF(q) is derived, where p and q are odd primes, and q is a primitive root modulo p
2. The third, we give a validity of the proposed algorithm, and also prove that there exists an error sequence e
N
, where the Hamming weight of e
N
is not greater than k, such that the linear complexity of (s + e)
N
reaches the k-error linear complexity c. We also present a numerical example to illustrate the algorithm. Finally, we present the minimum value k for which the k-error linear complexity is strictly less than the linear complexity. 相似文献
10.