Certain counterexamples to the construction of combinatorial designs on infinite sets.

Since Horadam and de Launey introduced the cocyclic framework on combinatorial designs in the 1990s, it has revealed itself as a powerful technique for looking for (cocyclic) Hadamard matrices. Ten years later, the series of papers by Kotsireas, Koukouvinos and Seberry about Hadamard matrices with one or two circulant cores introduced a different structured approach to the Hadamard conjecture. This paper is built on both strengths, so that Hadamard matrices with cocyclic cores are introduced and studied. They are proved to strictly include usual Hadamard matrices with one and two circulant cores, and therefore provide a wiser uniform approach to a structured Hadamard conjecture.

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Non-repetitive colorings of infinite sets

Discrete Mathematics ◽

10.1016/s0012-365x(02)00879-8 ◽

2003 ◽

Vol 265 (1-3) ◽

pp. 365-373 ◽

Cited By ~ 8

Author(s):

Jarosław Grytczuk ◽

Wiesław Śliwa

Keyword(s):

Infinite Sets

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Constructing Byzantine Quorum systems from combinatorial designs

Information Processing Letters ◽

10.1016/s0020-0190(99)00075-7 ◽

1999 ◽

Vol 71 (1) ◽

pp. 35-42 ◽

Cited By ~ 1

Author(s):

Tatsuhiro Tsuchiya ◽

Nobuhiko Ido ◽

Tohru Kikuno

Keyword(s):

Combinatorial Designs ◽

Quorum Systems

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Several classes of permutation trinomials from Niho exponents over finite fields of characteristic 3

Journal of Algebra and Its Applications ◽

10.1142/s0219498819500695 ◽

2019 ◽

Vol 18 (04) ◽

pp. 1950069

Author(s):

Qian Liu ◽

Yujuan Sun

Keyword(s):

Positive Integer ◽

Finite Field ◽

Coding Theory ◽

Permutation Polynomials ◽

Combinatorial Designs ◽

Dickson Polynomial ◽

Niho Exponents ◽

Characteristic 3 ◽

Permutation Trinomials ◽

Algebraic Forms

Permutation polynomials have important applications in cryptography, coding theory, combinatorial designs, and other areas of mathematics and engineering. Finding new classes of permutation polynomials is therefore an interesting subject of study. Permutation trinomials attract people’s interest due to their simple algebraic forms and additional extraordinary properties. In this paper, based on a seventh-degree and a fifth-degree Dickson polynomial over the finite field [Formula: see text], two conjectures on permutation trinomials over [Formula: see text] presented recently by Li–Qu–Li–Fu are partially settled, where [Formula: see text] is a positive integer.

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