On difference sets with small $$\lambda $$ λ
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DOI: 10.1007/s10801-020-00992-x
Abstract: In a 1989 paper, Arasu (Arch Math 53:622–624, 1989) used an observation about multipliers to show that no (352, 27, 2) difference set exists in any abelian group. The proof is quite short and required no computer… read more here.
Keywords: small lambda; difference sets; difference; show ... See more keywords
A proof from the book, perchance
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DOI: 10.1007/s10801-020-01007-5
Abstract: The fact that the groups $${\mathbb {Z}}_{2^m} \times {\mathbb {Z}}_{2^m}$$ Z 2 m × Z 2 m contain difference sets was first established by induction by Jim Davis in his Virginia dissertation of 1987. Later… read more here.
Keywords: book perchance; difference; difference sets; proof book ... See more keywords
A Construction of Minimal Linear Codes From Partial Difference Sets
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DOI: 10.1109/tit.2021.3067049
Abstract: In this paper, we study a class of linear codes defined by characteristic functions of certain subsets of a finite field. We derive a sufficient and necessary condition for such a code to be a… read more here.
Keywords: minimal linear; difference sets; partial difference; linear codes ... See more keywords
Constructing near-Hadamard designs with (almost) D-optimality by general supplementary difference sets
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DOI: 10.5705/ss.202014.0115
Abstract: We propose a new and unified construction method, general supplementary difference sets (GSDS)s, for near-Hadamard designs when the run sizes are n ≡ 2 (mod 4). These designs possess high D-efficiencies. Ehlich (1964) derived an… read more here.
Keywords: near hadamard; hadamard designs; difference sets; supplementary difference ... See more keywords