A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2012; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
New Cyclic Difference Sets with Singer Parameters Constructed from d-Homogeneous Functions

2004
*
Designs, Codes and Cryptography
*

In this paper, for a prime power q,

doi:10.1023/b:desi.0000036246.52472.81
fatcat:elf64mv6nva4vnl43xbmtdkzae
*new**cyclic**difference**sets**with**Singer**parameters*ððq n À 1=q À 1Þ; ðq nÀ1 À 1=q À 1Þ; ðq nÀ2 À 1=q À 1ÞÞ are*constructed*by using q-ary sequences (*d*-*homogeneous**functions*... When q is a power of 3,*new**cyclic**difference**sets**with**Singer**parameters*ððq n À 1=q À 1Þ; ðq nÀ1 À 1=q À 1Þ; ðq nÀ2 À 1=q À 1ÞÞ are*constructed**from*the ternary sequences of period q n À 1*with*ideal ... In this section, it is shown for a prime power q that*cyclic**difference**sets**with**Singer**parameter*can be*constructed**from*the*d*-*homogeneous**functions**with**difference*-balance property. ...##
###
New Cyclic Relative Difference Sets Constructed From$d$-Homogeneous Functions With Difference-Balanced Property

2005
*
IEEE Transactions on Information Theory
*

In this paper, for any prime power q, it is shown that

doi:10.1109/tit.2004.842712
fatcat:6bc4azywpvewjcvsnj54ne36ja
*new**cyclic*relative*difference**sets**with**parameters*( q n −1 q−1 , q−1, q n−1 , q n−2 ) can be*constructed*by using*d*-*homogeneous**functions*on F q ... Several*new**cyclic*relative*difference**sets**with**parameters*( q n −1 q−1 , q − 1, q n−1 , q n−2 ) are*constructed*by using p-ary sequences of period q n − 1*with*ideal autocorrelation property introduced ... No introduced the*construction*method of a*new**cyclic**difference**set**with**Singer**parameters**from*the*d*-*homogeneous**function**with**difference*-balanced property [8] . ...##
###
Difference Balanced Functions and Their Generalized Difference Sets
[article]

2013
*
arXiv
*
pre-print

In the literature, all existing such

arXiv:1309.7842v1
fatcat:ozpyylng6ffh3nujq4cqam7b2y
*functions*are associated*with*the*d*-*homogeneous*property, and it was conjectured by Gong and Song that*difference*balanced*functions*must be*d*-*homogeneous*. ... First we characterize*difference*balanced*functions*by generalized*difference**sets**with*respect to two exceptional subgroups. ... Furthermore, the projection ρ(*D*b ) is a*cyclic**difference**set**with**Singer**parameters*p n −1 p−1 , p n−1 , p n−2 (p − 1) for each b ∈ F * p and ρ(*D*0 ) is the complement of ρ(*D*b ), where ρ : F * p n → ...##
###
Recent progress in algebraic design theory

2005
*
Finite Fields and Their Applications
*

We survey recent results on

doi:10.1016/j.ffa.2005.06.003
fatcat:5v7swzvqpreijnuzd6z6uagulm
*difference**sets*, p-ranks and Smith normal forms of certain*set*-inclusion matrices and subspace-inclusion matrices. ... No [96] used*d*-*homogeneous**functions*on F * q m over F q*with**difference*-balanced property to*construct**cyclic**difference**sets**with*classical*parameters*. ...*Difference**sets**with*classical*parameters*The*Singer**difference**sets*arise*from*the classical designs of points and hyperplanes in projective space PG(m − 1, q); they are*cyclic**difference**sets**with**parameters*...##
###
Page 430 of Mathematical Reviews Vol. , Issue 85b
[page]

1985
*
Mathematical Reviews
*

At the same time, the authors

*construct*over 500000*new*, simple, nontrivial 5-designs*with*v = 33, by using the 4-*homogeneous*group PI'L2(32). Sanpe: Kageyama (Hiroshima) 85b:05033 85b:05034 ... A*Singer*design is a symmetric block design*with**parameters*(qr +q™-' + ---+qt1,q™-) + ---+q+1,q""? + ---+94+1),¢ a prime power. ...##
###
Formal solutions of differential equations

1990
*
Journal of symbolic computation
*

By using the term "formal", I wish to emphasize the fact that most of the time I will not be concerned

doi:10.1016/s0747-7171(08)80037-5
fatcat:rz54tv4j3jezxjxugn22mr4kji
*with*questions of where power series converge or in what domains the expressions represent*functions*... Consider the linear differential equation z(y) = an_l(x)y/n-1) + . . . + a0(x)Y = 0 This is an e x p a n*d*e*d*and revised version of talks presented at ... For example, C(x)*with*the derivation*d*/dx in a differential field as is the field of meromorphic*functions*on a connected open*set*in C*with*the usual derivation. ...##
###
Gauss Sums, Jacobi Sums, and p-ranks of Cyclic Difference Sets
[article]

1998
*
arXiv
*
pre-print

We study quadratic residue

arXiv:math/9807029v2
fatcat:vs5em2tsdrb2pbwnqz42yv22v4
*difference**sets*, GMW*difference**sets*, and*difference**sets*arising*from*monomial hyperovals, all of which are (2^*d*-1, 2^*d*-1-1, 2^*d*-2-1)*cyclic**difference**sets*in the multiplicative ... We determine the 2-ranks of the*difference**sets*arising*from*the Segre and Glynn hyperovals, in the following way. ... The research of the fourth was supported in part by NSA grant MDA 904-97-0104, and a grant*from*the University of Delaware Research Foundation. ...##
###
Gauss Sums, Jacobi Sums, and p-Ranks of Cyclic Difference Sets

1999
*
Journal of combinatorial theory. Series A
*

We study quadratic residue

doi:10.1006/jcta.1998.2950
fatcat:jkx5jmvmofc2rpe2myci3y2b3u
*difference**sets*, GMW*difference**sets*, and*difference**sets*arising*from*monomial hyperovals, all of which are (2*d*− 1, 2*d*−1 − 1, 2*d*−2 − 1)*cyclic**difference**sets*in the finite ... We determine the 2-ranks of the*difference**sets*arising*from*the Segre and Glynn hyperovals, in the following way. ... The research of the fourth was supported in part by NSA grant MDA 904-97-0104, and a grant*from*the University of Delaware Research Foundation. ...##
###
Orbit codes from forms on vector spaces over a finite field

2019
*
Advances in Mathematics of Communications
*

In this paper we

doi:10.3934/amc.2020105
fatcat:udkkhljsxvh6fkcgbinp5i546m
*construct**different*families of orbit codes in the vector spaces of the symmetric bilinear forms, quadratic forms and Hermitian forms on an n-dimensional vector space over the finite field ... In this paper we aim at establishing*new*techniques for the*construction*of orbit codes. ... Note that for k ≤ n − k, starting*from*a suitable*set*of k × (n − k)-matrices*with*entries in F q , known as MRD-codes, by means of the so-called lifting process, one can*construct*an (n, q (n−k)(k−*d*+1 ...##
###
On Rational Solutions of Systems of Linear Differential Equations

1999
*
Journal of symbolic computation
*

We propose a

doi:10.1006/jsco.1999.0314
fatcat:xqpgeyuhnvctdbl7vciwmrljsu
*new*algorithm to compute the*set*of rational solutions of such a system. This algorithm does not require the use of*cyclic*vectors. ... We show how one can use this algorithm to give a method to find the*set*of solutions*with*entries in K(x)[log x] of M(Y ) = N . ... One then obtains a*new**set*of*parameters*P, a*set*C of linear constraints on these*parameters*and a polynomial sol = x µ c µ where the c µ 's are column vectors, the components of which are linear in the ...##
###
Ring geometries, Two-Weight Codes and Strongly Regular Graphs
[article]

2007
*
arXiv
*
pre-print

These examples all yield infinite families of strongly regular graphs

arXiv:0709.0862v1
fatcat:umhmpehjdjcgrdtvg7bdrhxl2u
*with*non-trivial*parameters*. ... Here we extend this classical result to the case of a ring-linear code*with*exactly two nonzero*homogeneous*weights and multisets of points in an associated projective ring geometry. ... These point*sets*provide*new**constructions*of non-trivial strongly regular graphs. ...##
###
Ring geometries, two-weight codes, and strongly regular graphs

2008
*
Designs, Codes and Cryptography
*

These examples all yield infinite families of strongly regular graphs

doi:10.1007/s10623-007-9136-8
fatcat:3i7b3d6zhrfwxbhywmmleadq6q
*with*non-trivial*parameters*. ... Here we extend this classical result to the case of a ring-linear code*with*exactly two nonzero*homogeneous*weights and multisets of points in an associated projective ring geometry. ... These point*sets*provide*new**constructions*of non-trivial strongly regular graphs. ...##
###
Further combinatorial constructions for optimal frequency-hopping sequences

2006
*
Journal of combinatorial theory. Series A
*

Theory 50 (2004) 2408-2420]

doi:10.1016/j.jcta.2006.03.019
fatcat:663deipeabgjnapcuxrksjysfe
*from*a combinatorial approach, where a correspondence between frequency-hopping (FH) sequences and partition-type*cyclic**difference*packings was established, and several combinatorial ...*constructions*were provided for FHMA systems*with*a single optimal FH sequence. ... Zhu at Suzhou University for their helpful discussions on the*constructions*in Sections 4 and 6, respectively, and the two anonymous referees for their helpful comments. ...##
###
The family index theorem and bifurcation of solutions of nonlinear elliptic bvp
[article]

2012
*
arXiv
*
pre-print

The results are of

arXiv:1107.1727v3
fatcat:2dppb3c52bevtjyjjcycwbg3di
*different*nature*from*the ones that can be obtained via the traditional Lyapunov-Schmidt reduction. ... Our sufficient conditions for bifurcation are derived*from*the Atiyah-*Singer*family index theorem and therefore they depend only on the coefficients of derivatives of leading order of the linearized differential ... Then the approximations are*constructed*using the fact that the*set*of restrictions to the unit sphere of elements of A(n, r) = ∪ k≥0 A(n, r, 2k) is dense in the*set*of even continuos*functions**from*the ...##
###
Linear Codes from Some 2-Designs
[article]

2015
*
arXiv
*
pre-print

In this paper, a

arXiv:1503.06511v1
fatcat:4c2m5zgge5g33bnol32vdxsst4
*different*method of*constructing*linear codes using specific classes of 2-designs is studied, and linear codes*with*a few weights are obtained*from*almost*difference**sets*,*difference**sets*... A classical method of*constructing*a linear code over (q)*with*a t-design is to use the incidence matrix of the t-design as a generator matrix over (q) of the code. ... Sihem Mesnager, for their*constructive*comments that much improved the presentation and quality of this paper. ...
« Previous

*Showing results 1 — 15 out of 2,564 results*