On the maximal number of factors and the enumeration of 3-symbol orthogonal arrays of strength 3 and index 2

Hedayat, A.; Seiden, Esther; Stufken, John

doi:10.1016/s0378-3758(96)00059-6

Cited by 23 publications

(8 citation statements)

References 2 publications

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“…The same authors give the number of non-isomorphic OA(48; 4 1 3 1 2 4 ; 3) and OA(54; 3 5 2 1 ; 3). The four OA(54; 3 5 ; 3) were derived by Hedayat et al [12]. All classes for the factor sets 2 4 and 2 5 and any N are given by Seiden and Zemach [21] and Stufken and Tang [24], respectively.…”

Section: Strength-3 Arraysmentioning

confidence: 99%

Complete enumeration of pure‐level and mixed‐level orthogonal arrays

Schoen

Eendebak

Nguyen

2009

J of Combinatorial Designs

111

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We specify an algorithm to enumerate a minimum complete set of combinatorially non-isomorphic orthogonal arrays of given strength t, run-size N, and level-numbers of the factors. The algorithm is the first one handling general mixed-level and pure-level cases. Using an implementation in C, we generate most non-trivial series for t = 2, N ≤ 28, t = 3, N ≤ 64, and t = 4, N ≤ 168. The exceptions define limiting run-sizes for which the algorithm returns complete sets in a reasonable amount of time. q

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Section: Strength-3 Arraysmentioning

confidence: 99%

Complete enumeration of pure‐level and mixed‐level orthogonal arrays

Schoen

Eendebak

Nguyen

2009

J of Combinatorial Designs

111

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“…q = 3: (14, 4)-coloring in H(7, 3) -: if such a coloring exists then each 5-dimensional face of H(7, 3) contains an orthogonal array A with certain parameters. Nonexistence of such array A follows from [14]. q = 6: (35, 1)-coloring in H(7, 6) -: there are no 1-perfect codes in H(7, 6) [13].…”

Section: Appendix Perfect Colorings In Hamming Graphs Of Small Sizesmentioning

confidence: 99%

Perfect 2-colorings of Hamming graphs

Bespalov,

Krotov,

Matiushev

et al. 2019

Preprint

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We consider the problem of existence of perfect 2-colorings of Hamming graphs with given parameters. We start with conditions on parameters of graphs and colorings that are necessary for their existence. Next we observe constructions of perfect colorings, including some new constructions giving new parameters of colorings. At last, we deduce which parameters of colorings are covered by these constructions and give tables of admissible parameters of 2-colorings in Hamming graphs H(n, q) for small n and q.

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“…As is often the case, OAs can be very useful for quantum information theory [22,41,42,43]. Recently, many new construction methods of MOAs with high strength have been provided [44,45,46,47,48,49,50,51,52,53,54]. Such new developments in MOAs make it possible to obtain infinitely many new k-uniform states in heterogeneous systems from IrMOAs.…”

Section: Introductionmentioning

confidence: 95%

Quantum k-uniform states for heterogeneous systems from irredundant mixed orthogonal arrays

Pang,

Zhang,

Fei

et al. 2021

Preprint

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Quantum multipartite entangled states play significant roles in quantum information processing. By using difference schemes and orthogonal partitions, we construct a series of infinite classes of irredundant mixed orthogonal arrays (IrMOAs) and thus provide positive answers to two open problems. The first is the extension of the method for constructing homogeneous systems from orthogonal arrays (OAs) to heterogeneous multipartite systems with different individual levels. The second is the existence of k-uniform states in heterogeneous quantum systems. We present explicit constructions of two and three-uniform states for arbitrary heterogeneous multipartite systems with coprime individual levels, and characterize the entangled states in heterogeneous systems consisting of subsystems with nonprime power dimensions as well. Moreover, we obtain infinite classes of k-uniform states for heterogeneous multipartite systems for any k ≥ 2. The non-existence of a class of IrMOAs is also proved.

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On the maximal number of factors and the enumeration of 3-symbol orthogonal arrays of strength 3 and index 2

Cited by 23 publications

References 2 publications

Complete enumeration of pure‐level and mixed‐level orthogonal arrays

Complete enumeration of pure‐level and mixed‐level orthogonal arrays

Perfect 2-colorings of Hamming graphs

Quantum k-uniform states for heterogeneous systems from irredundant mixed orthogonal arrays

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