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Divisible difference sets, relative difference sets and sequences with ideal autocorrelation
Information Sciences, 2013 In this correspondence, we consider the equivalent condition that a sequence possesses ideal autocorrelation function. As we know, for a binary sequence, the equivalent condition is that the characteristic class of this sequence consists of two cyclic ...
Tongjiang Yan, Guozhen Xiao
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The Quarterly Journal of Mathematics, 1963
A set of \(m+1\) integers \(k_0, k_1,\dots,k_m\) with the property that the \(m^2+m\) differences \(k_i-k_j\) \((i\neq j\), \(i, j=1, 2, \dots, m)\) are congruent modulo \(q\), \(q = m^2 + m + 1\), to the integers \(1, 2, \dots, m^2+m\) in some order is called a perfect difference set.
Halberstam, H., Laxton, R. R.
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A set of \(m+1\) integers \(k_0, k_1,\dots,k_m\) with the property that the \(m^2+m\) differences \(k_i-k_j\) \((i\neq j\), \(i, j=1, 2, \dots, m)\) are congruent modulo \(q\), \(q = m^2 + m + 1\), to the integers \(1, 2, \dots, m^2+m\) in some order is called a perfect difference set.
Halberstam, H., Laxton, R. R.
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Canadian Journal of Mathematics, 1979
1. Introduction. Let A be a sequence; throughout this paper sequences are understood to be infinite, strictly increasing and composed of non-negative integers. We define D, the infinite-difference set of A, to be the set of those non-negative integers which occur infinitely often as the difference of two terms of A.
Stewart, C. L., Tijdeman, R.
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1. Introduction. Let A be a sequence; throughout this paper sequences are understood to be infinite, strictly increasing and composed of non-negative integers. We define D, the infinite-difference set of A, to be the set of those non-negative integers which occur infinitely often as the difference of two terms of A.
Stewart, C. L., Tijdeman, R.
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Optimal and perfect difference systems of sets
Journal of Combinatorial Theory - Series A, 2009 Difference systems of sets (DSS) were introduced in 1971 by Levenstein for the construction of codes for synchronization, and are closely related to cyclic difference families.
Ding, Cunsheng
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A Construction of Difference Sets
Designs, Codes and Cryptography, 1998The paper gives a construction of a family of difference sets with parameters \[ v=4q^{2n+2} {q^{2n+2} -1\over q^2-1}, \quad k=q^{2n+2} \left({2 (q^{2n+2} -1)\over q+1} +1\right), \quad \lambda= (q^{2n+2} -q^{2n+1}) {q^{2n+1} +1\over q+1} \] in a group of the form \(K\times G\), where \(G\) is an abelian 2-group of order \(4q^{2n+2}\) which contains an
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Canadian Journal of Mathematics, 1958
A difference set (,D) is defined in (2) as a subset D of k elements in a group of order υ with the following properties :(1) if x ∊ , x ≠ 1, there are exactly λ distinct ordered pairs (d1d2) of elements of D such that x = 1d2;(2) if x ∊ , x ≠ 1, there are exactly λ distinct ordered pairs (3d4) of elements of D such that x = 3d4−1.
Stanton, R. G., Sprott, D. A.
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A difference set (,D) is defined in (2) as a subset D of k elements in a group of order υ with the following properties :(1) if x ∊ , x ≠ 1, there are exactly λ distinct ordered pairs (d1d2) of elements of D such that x = 1d2;(2) if x ∊ , x ≠ 1, there are exactly λ distinct ordered pairs (3d4) of elements of D such that x = 3d4−1.
Stanton, R. G., Sprott, D. A.
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On the difference of fuzzy sets
International Journal of Intelligent Systems, 2008The paper deals with the concept of difference between fuzzy sets. Its main goal is to extend the model (and properties) of the difference relation from the class of classical crisp sets to their fuzzy analogues. Using the concept of triangular norm, a variety of such relations are suggested and analyzed.
Claudi Alsina, Enric Trillas
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Archiv der Mathematik, 1987
We generalize a theorem of Ghinelli-Smit on abelian projective planes and obtain a nonexistence theorem for (v,k,\(\lambda)\) abelian difference sets.
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We generalize a theorem of Ghinelli-Smit on abelian projective planes and obtain a nonexistence theorem for (v,k,\(\lambda)\) abelian difference sets.
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Multipliers of Difference Sets
Canadian Journal of Mathematics, 1963Let λ, K, v be integers such that 0 < λ < k < v. Then the set of integersis a difference set with parameters v, k, λ if each non-zero residue modulo v occurs precisely λ times and zero occurs precisely k times among the k2 ...
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Bulletin of the London Mathematical Society, 2000
Summary: Let \(p\), \(q\) be distinct and odd primes, and let \(a\), \(b\) be positive integers. In this paper we prove that if \(S(p^a,q^b)\) is a Storer difference set with the parameters \(v= p^aq^b\), \(k= (v-1)/4\) and \(\lambda= (v-5)/16\), then we have \[ a= b=1,\qquad p= (\rho^{3^r}+ \overline\rho^{3^r}- 1)/3,\qquad q= \rho^{3^r}+ \overline\rho^
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Summary: Let \(p\), \(q\) be distinct and odd primes, and let \(a\), \(b\) be positive integers. In this paper we prove that if \(S(p^a,q^b)\) is a Storer difference set with the parameters \(v= p^aq^b\), \(k= (v-1)/4\) and \(\lambda= (v-5)/16\), then we have \[ a= b=1,\qquad p= (\rho^{3^r}+ \overline\rho^{3^r}- 1)/3,\qquad q= \rho^{3^r}+ \overline\rho^
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