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On Amicable Sequences And Orthogonal Designs, S. Georgiou, C. Koukouvinos, Jennifer Seberry
On Amicable Sequences And Orthogonal Designs, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
In this paper we give a general theorem which can be used to multiply the length of amicable sequences keeping the amicability property and the type of the sequences. As a consequence we have that if there exist two, four or eight amicable sequences of length m and type (al, a2), (al, a2, a3, a4) or (al, a2, ... , a8) then there exist amicable sequences of length ℓ ≡ 0 (mod m) and of the same type. We also present a theorem that produces a set of 2v amicable sequences from a set of v (not necessary amicable) sequences …
On Full Orthogonal Designs In Order 56, S. Georgiou, C. Koukouvinos, Jennifer Seberry
On Full Orthogonal Designs In Order 56, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
We find new full orthogonal designs in order 56 and show that of 1285 possible OD(56; s1, s2, s3, 56—s1—s2-s3) 163 are known, of 261 possible OD(56; s1, s2, 56—s1—s2) 179 are known. All possible OD(56; s1, 56 — s1) are known.
On Full Orthogonal Designs In Order 72, S. Georgiou, C. Koukouvinos, Jennifer Seberry
On Full Orthogonal Designs In Order 72, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Professor Jennifer Seberry
We find new full orthogonal designs in order 72 and show that of 2700 possible OD(72; s1, s2, s3, 72—s1—s2—s3) 335 are known, of 432 possible OD(72; s1, s2, 72—si—s2) 308 are known. All possible OD(72; s1, 72 — s1) are known.
On Full Orthogonal Designs In Order 72, S. Georgiou, C. Koukouvinos, Jennifer Seberry
On Full Orthogonal Designs In Order 72, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We find new full orthogonal designs in order 72 and show that of 2700 possible OD(72; s1, s2, s3, 72—s1—s2—s3) 335 are known, of 432 possible OD(72; s1, s2, 72—si—s2) 308 are known. All possible OD(72; s1, 72 — s1) are known.
Some Results On Kharaghani Type Orthogonal Designs, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Some Results On Kharaghani Type Orthogonal Designs, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
In this paper we give a general theorem which can be used to multiply the length of amicable sequences keeping the amicability property and the type of the sequences. As a consequence we have that if there exist two, four or eight amicable sequences of length m and type (al, a2), (al, a2, a3, a4) or (al, a2, …, as) then there exist amicable sequences of length ℓ ≡ 0 (mod m) and of the same type. We also present a theorem that produces a set of 2v amicable sequences from a set of v (not necessary amicable) sequences and …
On Full Orthogonal Designs In Order 56, S. Georgiou, C. Koukouvinos, Jennifer Seberry
On Full Orthogonal Designs In Order 56, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
We find new full orthogonal designs in order 56 and show that of 1285 possible OD(56; s1, s2, s3, 56—s1—s2-s3) 163 are known, of 261 possible OD(56; s1, s2, 56—s1—s2) 179 are known. All possible OD(56; s1, 56 — s1) are known.
Short Amicable Sets, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Short Amicable Sets, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
Abstract: A pair of matrices X and Y are said to be amicable if XYT = YXT. In this paper, if X and Y are orthogonal designs, group generated or circulant on the group G, these will be denoted 2—SAS(n; ul, u2; G). Recently Kharaghani, in "Arrays for orthogonal designs", J. Combin. Designs, 8 (2000), 166-173, extended this concept to an amicable set, {Ai}2n, i=1, of 2n circulant matrices, which satisfy ∑(Aσ(2i-1)AT σ(2i-1) - Aσ(2i) AT (2i-1) = 0. In this paper we concentrate on constructing short amicable sets, which satisfy the same equation but contain four, called short, or …
On Amicable Sequences And Orthogonal Designs, S. Georgiou, C. Koukouvinos, Jennifer Seberry
On Amicable Sequences And Orthogonal Designs, S. Georgiou, C. Koukouvinos, Jennifer Seberry
Faculty of Informatics - Papers (Archive)
In this paper we give a general theorem which can be used to multiply the length of amicable sequences keeping the amicability property and the type of the sequences. As a consequence we have that if there exist two, four or eight amicable sequences of length m and type (al, a2), (al, a2, a3, a4) or (al, a2, ... , a8) then there exist amicable sequences of length ℓ ≡ 0 (mod m) and of the same type. We also present a theorem that produces a set of 2v amicable sequences from a set of v (not necessary amicable) sequences …