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New Cyclic Difference Sets with Singer Parameters Constructed from d-Homogeneous Functions
2004
Designs, Codes and Cryptography
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In this paper, for a prime power q, 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. ...
doi:10.1023/b:desi.0000036246.52472.81
fatcat:elf64mv6nva4vnl43xbmtdkzae
New Cyclic Relative Difference Sets Constructed From$d$-Homogeneous Functions With Difference-Balanced Property
2005
IEEE Transactions on Information Theory
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In this paper, for any prime power q, it is shown that 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] . ...
doi:10.1109/tit.2004.842712
fatcat:6bc4azywpvewjcvsnj54ne36ja
Difference Balanced Functions and Their Generalized Difference Sets
[article]
2013
arXiv
pre-print
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In the literature, all existing such 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 → ...
arXiv:1309.7842v1
fatcat:ozpyylng6ffh3nujq4cqam7b2y
Recent progress in algebraic design theory
2005
Finite Fields and Their Applications
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We survey recent results on 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 ...
doi:10.1016/j.ffa.2005.06.003
fatcat:5v7swzvqpreijnuzd6z6uagulm
Page 430 of Mathematical Reviews Vol. , Issue 85b
[page]
1985
Mathematical Reviews
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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
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By using the term "formal", I wish to emphasize the fact that most of the time I will not be concerned 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. ...
doi:10.1016/s0747-7171(08)80037-5
fatcat:rz54tv4j3jezxjxugn22mr4kji
Gauss Sums, Jacobi Sums, and p-ranks of Cyclic Difference Sets
[article]
1998
arXiv
pre-print
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We study quadratic residue 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. ...
arXiv:math/9807029v2
fatcat:vs5em2tsdrb2pbwnqz42yv22v4
Gauss Sums, Jacobi Sums, and p-Ranks of Cyclic Difference Sets
1999
Journal of combinatorial theory. Series A
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We study quadratic residue 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. ...
doi:10.1006/jcta.1998.2950
fatcat:jkx5jmvmofc2rpe2myci3y2b3u
Orbit codes from forms on vector spaces over a finite field
2019
Advances in Mathematics of Communications
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In this paper we 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 ...
doi:10.3934/amc.2020105
fatcat:udkkhljsxvh6fkcgbinp5i546m
On Rational Solutions of Systems of Linear Differential Equations
1999
Journal of symbolic computation
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We propose a 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 ...
doi:10.1006/jsco.1999.0314
fatcat:xqpgeyuhnvctdbl7vciwmrljsu
Ring geometries, Two-Weight Codes and Strongly Regular Graphs
[article]
2007
arXiv
pre-print
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These examples all yield infinite families of strongly regular graphs 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. ...
arXiv:0709.0862v1
fatcat:umhmpehjdjcgrdtvg7bdrhxl2u
Ring geometries, two-weight codes, and strongly regular graphs
2008
Designs, Codes and Cryptography
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These examples all yield infinite families of strongly regular graphs 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. ...
doi:10.1007/s10623-007-9136-8
fatcat:3i7b3d6zhrfwxbhywmmleadq6q
Further combinatorial constructions for optimal frequency-hopping sequences
2006
Journal of combinatorial theory. Series A
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Theory 50 (2004) 2408-2420] 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. ...
doi:10.1016/j.jcta.2006.03.019
fatcat:663deipeabgjnapcuxrksjysfe
The family index theorem and bifurcation of solutions of nonlinear elliptic bvp
[article]
2012
arXiv
pre-print
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The results are of 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 ...
arXiv:1107.1727v3
fatcat:2dppb3c52bevtjyjjcycwbg3di
Linear Codes from Some 2-Designs
[article]
2015
arXiv
pre-print
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In this paper, a 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. ...
arXiv:1503.06511v1
fatcat:4c2m5zgge5g33bnol32vdxsst4
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