共查询到20条相似文献,搜索用时 356 毫秒
1.
Jong-Seon No 《Designs, Codes and Cryptography》2004,33(3):199-213
In this paper, for a prime power q, new cyclic difference sets with Singer para- meters ((q
n
–1/q–1), (q
n–1–1/q–1), (q
n–2–1/q–1)) are constructed by using q-ary sequences (d-homogeneous functions) of period q
n
–1 and the generalization of GMW difference sets is proposed by combining the generation methods of d-form sequences and extended sequences. When q is a power of 3, new cyclic difference sets with Singer parameters ((q
n
–1/q–1), (q
n–1–1/q–1), (q
n–2–1/q–1)) are constructed from the ternary sequences of period q
n
–1 with ideal autocorrelation introduced by Helleseth, Kumar, and Martinsen. 相似文献
2.
Given N = (q
m
− 1)/(q − 1), where q is a power of a prime, q > 2, we present two constructions of different partitions of the set F
q
N
of all q-ary length N vectors into perfect q-ary codes of length N. The lower bounds on the number of these partitions are presented. 相似文献
3.
In this paper, by means of a new idea, the concept of (invertible) (∈,∈∨q)-fuzzy n-ary subhypergroups of a commutative n-ary hypergroup is introduced and some related properties are investigated. A kind of n-ary quotient hypergroup by an (∈, ∈∨q)-fuzzy n-ary subhypergroup is provided and the relationships among (∈, ∈∨q)-fuzzy n-ary subhypergroups, n-ary quotient hypergroups and homomorphism are investigated. Several isomorphism theories of n-ary hypergroups are established. 相似文献
4.
S. A. Malyugin 《Journal of Applied and Industrial Mathematics》2010,4(2):218-230
The nonsystematic perfect q-ary codes over finite field F
q
of length n = (q
m
− 1)/(q − 1) are constructed in the case when m ≥ 4 and q ≥ 2 and also when m = 3 and q is not prime. For q ≠ 3, 5, these codes can be constructed by switching seven disjoint components of the Hamming code H
q
n
; and, for q = 3, 5, eight disjoint components. 相似文献
5.
Guang Gong 《Discrete Applied Mathematics》2006,154(18):2590-2598
Let p be a prime, q=pm and Fq be the finite field with q elements. In this paper, we will consider q-ary sequences of period qn-1 for q>2 and study their various balance properties: symbol-balance, difference-balance, and two-tuple-balance properties. The array structure of the sequences is introduced, and various implications between these balance properties and the array structure are proved. Specifically, we prove that if a q-ary sequence of period qn-1 is difference-balanced and has the “cyclic” array structure then it is two-tuple-balanced. We conjecture that a difference-balanced q-ary sequence of period qn-1 must have the cyclic array structure. The conjecture is confirmed with respect to all of the known q-ary sequences which are difference-balanced, in particular, which have the ideal two-level autocorrelation function when q=p. 相似文献
6.
Johannes F. Morgenbesser 《The Ramanujan Journal》2012,27(1):43-70
Let q=−a±i and denote by s
q
the complex sum-of-digits function. We show that the sequence (αs
q
(p)) running over all Gaussian primes lying in a circular sector is uniformly distributed modulo 1 if and only if α is irrational. Moreover, we prove that the sum-of-digits function of primes is well distributed in arithmetic progressions.
This work generalizes a theorem of Mauduit and Rivat that was the solution of a long-standing conjecture by Gelfond concerning
the usual q-ary sum-of-digits function. It improves also a result of Drmota, Rivat, and Stoll, who could only deal with sufficiently
large prime bases q=−a±i and the full disc. 相似文献
7.
Both R. Games [4] and V.P. Ipatov [8] have given constructions for perfect ternary sequences. Games uses difference sets and quadrics in projective space, while Ipatov uses q-ary m-sequences. We show that the Ipatov sequences are a subset of the Games sequences. Further, we show that a conjecture of Games relating to quadrics in projective spaces does not hold in general. 相似文献
8.
Michel Lavrauw Leo Storme Geertrui Van de Voorde 《Designs, Codes and Cryptography》2008,48(3):231-245
In this paper, we study the p-ary linear code C(PG(n,q)), q = p
h
, p prime, h ≥ 1, generated by the incidence matrix of points and hyperplanes of a Desarguesian projective space PG(n,q), and its dual code. We link the codewords of small weight of this code to blocking sets with respect to lines in PG(n,q) and we exclude all possible codewords arising from small linear blocking sets. We also look at the dual code of C(PG(n,q)) and we prove that finding the minimum weight of the dual code can be reduced to finding the minimum weight of the dual
code of points and lines in PG(2,q). We present an improved upper bound on this minimum weight and we show that we can drop the divisibility condition on the
weight of the codewords in Sachar’s lower bound (Geom Dedicata 8:407–415, 1979).
G. Van de Voorde’s research was supported by the Institute for the Promotion of Innovation through Science and Technology
in Flanders (IWT-Vlaanderen). 相似文献
9.
In this paper, we study the weighted (x(q + 1), x; 2, q)-minihypers. These are weighted sets of x(q + 1) points in PG(2, q) intersecting every line in at least x points. We investigate the decomposability of these minihypers, and define a switching construction which associates to an
(x(q + 1), x; 2, q)-minihyper, with x ≤ q
2 − q, not decomposable in the sum of another minihyper and a line, a (j(q + 1), j; 2, q)-minihyper, where j = q
2 − q − x, again not decomposable into the sum of another minihyper and a line. We also characterize particular (x(q + 1), x; 2, q)-minihypers, and give new examples. Additionally, we show that (x(q + 1), x; 2, q)-minihypers can be described as rational sums of lines. In this way, this work continues the research on (x(q + 1), x; 2, q)-minihypers by Hill and Ward (Des Codes Cryptogr 44:169–196, 2007), giving further results on these minihypers. 相似文献
10.
A. M. Romanov 《Journal of Applied and Industrial Mathematics》2012,6(3):355-359
In this paper, the properties of the i-components of Hamming codes are described. We suggest constructions of the admissible families of components of Hamming codes. Each q-ary code of length m and minimum distance 5 (for q = 3, the minimum distance is 3) is shown to embed in a q-ary 1-perfect code of length n = (q m − 1)/(q − 1). Moreover, each binary code of length m+k and minimum distance 3k + 3 embeds in a binary 1-perfect code of length n = 2 m − 1. 相似文献
11.
Lijun Ji 《Designs, Codes and Cryptography》2007,45(1):39-49
Recently, Franek et al. introduced large sets of v − 1 L-intersecting Steiner triple systems of order v (STS(v)) and gave four constructions for them (Des., Codes and Cryptogr., 26 (2002), 243–256). In this paper, we mainly focus on
large sets of v − 1{0, 1}-intersecting STS(v) and large sets of v + 1{1}-intersecting STS(v). For this purpose, we introduce a concept of L-intersecting partitionable candelabra system (L-PCS) of order v with q(v) subsystems and establish a relationship between L-PCS and large set of q(v)L-intersecting STS(v). Some constructions for L-PCSs are also presented by 3-wise balanced designs. These facilitate the production of some new infinite classes of these large
sets.
Research supported by Tianyuan Mathematics Foundation of NSFC Grant 10526032 and Natural Science Foundation of Universities
of Jiangsu Province Grant 05KJB110111. 相似文献
12.
P. A. Valinevih 《Journal of Mathematical Sciences》2010,168(6):811-819
We propose a method for construction of the general solution of the Yang–Baxter equation with the U
q
(sℓ
n
) symmetry algebra. This method is based on the factorization property of the corresponding L-operator. We present a closed-form expression for the universal R-matrix in the form of a difference operator acting on the
space of functions of n(n − 1) variables. Bibliography: 16 titles. 相似文献
13.
E. J. Cheon 《Designs, Codes and Cryptography》2009,51(1):9-20
In this paper, we determine the smallest lengths of linear codes with some minimum distances. We construct a [g
q
(k, d) + 1, k, d]
q
code for sq
k-1 − sq
k-2 − q
s
− q
2 + 1 ≤ d ≤ sq
k-1 − sq
k-2 − q
s
with 3 ≤ s ≤ k − 2 and q ≥ s + 1. Then we get n
q
(k, d) = g
q
(k, d) + 1 for (k − 2)q
k-1 − (k − 1)q
k-2 − q
2 + 1 ≤ d ≤ (k − 2)q
k-1 − (k − 1)q
k-2, k ≥ 6, q ≥ 2k − 3; and sq
k-1 − sq
k-2 − q
s
− q + 1 ≤ d ≤ sq
k-1 − sq
k-2 − q
s
, s ≥ 2, k ≥ 2s + 1 and q ≥ 2s − 1.
This work was partially supported by the Com2MaC-SRC/ERC program of MOST/KOSEF (grant # R11-1999-054) and was partially supported by the Korea Research Foundation Grant funded by the Korean Government(MOEHRD)(KRF-2005-214-C00175). 相似文献
14.
Andrew Raich 《Mathematische Annalen》2010,348(1):81-117
The purpose of this article is to study compactness of the complex Green operator on CR manifolds of hypersurface type. We
introduce (CR-P
q
), a potential theoretic condition on (0, q)-forms that generalizes Catlin’s property (P
q
) to CR manifolds of arbitrary codimension. We prove that if an embedded CR-manifold of hypersurface type of real dimension
at least five satisfies (CR-P
q
) and (CR-P
n-1-q
), then the complex Green operator is a compact operator on the Sobolev spaces Hs0,q(M){H^s_{0,q}(M)} and Hs0,n-1-q(M){H^s_{0,n-1-q}(M)} , if 1 ≤ q ≤ n−2 and s ≥ 0. We use CR-plurisubharmonic functions to build a microlocal norm that controls the totally real direction of the tangent
bundle. 相似文献
15.
K. L. Rychkov 《Journal of Applied and Industrial Mathematics》2011,5(2):290-295
A generalization of the concept of parallel-sequential switching circuits (π-circuits) to the case when the variables assigned to contacts can take not two, as in the Boolean case, but a greater number of values.
The conductivity of the contact is still two-valued (the contact is either closed or open). A lower bound is obtained on the
complexity of these circuits computing the q-ary counter of multiplicity q, i.e., the function φ
q
: {0, 1, …, q − 1}
n
→ {0, 1} that equals 1 if the sum of values of its variables is a multiple of q. 相似文献
16.
Darryn Bryant Judith Egan Barbara Maenhaut Ian M. Wanless 《Designs, Codes and Cryptography》2009,50(1):93-105
In this paper, we present two constructions of divisible difference sets based on skew Hadamard difference sets. A special
class of Hadamard difference sets, which can be derived from a skew Hadamard difference set and a Paley type regular partial
difference set respectively in two groups of orders v
1 and v
2 with |v
1 − v
2| = 2, is contained in these constructions. Some result on inequivalence of skew Hadamard difference sets is also given in
the paper. As a consequence of Delsarte’s theorem, the dual set of skew Hadamard difference set is also a skew Hadamard difference
set in an abelian group. We show that there are seven pairwisely inequivalent skew Hadamard difference sets in the elementary
abelian group of order 35 or 37, and also at least four pairwisely inequivalent skew Hadamard difference sets in the elementary abelian group of order 39. Furthermore, the skew Hadamard difference sets deduced by Ree-Tits slice symplectic spreads are the dual sets of each other
when q ≤ 311.
相似文献
17.
In this paper, we construct three ternary linear codes associated with the orthogonal group O
−
(2, q) and the special orthogonal groups SO
−
(2, q) and SO
−
(4, q). Here q is a power of three. Then we obtain recursive formulas for the power moments of Kloosterman sums with square arguments and
for the even power moments of those in terms of the frequencies of weights in the codes. This is done via Pless power moment
identity and by utilizing the explicit expressions of “Gauss sums” for the orthogonal and special orthogonal groups O
−
(2n, q) and SO
−
(2n, q). 相似文献
18.
This work examines the existence of (4q
2,2q
2−q,q
2−q) difference sets, for q=p
f
, where p is a prime and f is a positive integer. Suppose that G is a group of order 4q
2 which has a normal subgroup K of order q such that G/K
≅
C
q
×C
2×C
2, where C
q
,C
2 are the cyclic groups of order q and 2 respectively. Under the assumption that p is greater than or equal to 5, this work shows that G does not admit (4q
2,2q
2−q,q
2−q) difference sets. 相似文献
19.
David G. Glynn 《Designs, Codes and Cryptography》2011,58(2):215-218
There is polynomial function X
q
in the entries of an m × m(q − 1) matrix over a field of prime characteristic p, where q = p
h
is a power of p, that has very similar properties to the determinant of a square matrix. It is invariant under multiplication on the left
by a non-singular matrix, and under permutations of the columns. This gives a way to extend the invariant theory of sets of
points in projective spaces of prime characteristic, to make visible hidden structure. There are connections with coding theory,
permanents, and additive bases of vector spaces. 相似文献
20.
We discuss the L
p
− L
q
mapping property of k-plane transforms acting on radial functions in certain weighted L
p
spaces with power weight. We show that for all admissible power weights it is not always possible to get strong (p, q) boundedness of the k-plane transform. However, we prove the best possible estimates with respect to the Lorentz norms. 相似文献