Finite field constructions of combinatorial arrays

Moura, Lucia; Mullen, Gary L.; Panario, Daniel

doi:10.1007/s10623-015-0152-9

Cited by 9 publications

(4 citation statements)

References 39 publications

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“…Ordered orthogonal arrays are related to classical combinatorial designs, namely, covering arrays (CAs) and orthogonal arrays (OAs). We refer the reader to a survey paper by Colbourn [11] on CAs, a book by Hedayat et al [17] on OAs, and a survey paper by Moura et al [22, Section 3] for their relations to ordered orthogonal arrays.…”

Section: Preliminariesmentioning

confidence: 99%

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Ordered covering arrays and upper bounds on covering codes

Castoldi

Carmelo

Moura

et al. 2023

J of Combinatorial Designs

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This work shows several direct and recursive constructions of ordered covering arrays (OCAs) using projection, fusion, column augmentation, derivation, concatenation, and Cartesian product. Upper bounds on covering codes in Niederreiter-Rosenbloom-Tsfasman (shorten by NRT) spaces are also obtained by improving a general upper bound. We explore the connection between ordered covering arrays and covering codes in NRT spaces, which generalize similar results for the Hamming metric. Combining the new upper bounds for covering codes in NRT spaces and ordered covering arrays, we improve upper bounds on covering codes in NRT spaces for larger alphabets. We give tables comparing the new upper bounds for covering codes to existing ones.

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Section: Preliminariesmentioning

confidence: 99%

“…3], see also [13, Section VI.59.3]. For a survey of finite field constructions of OAs, CAs, and OOAs, see Moura et al [22, Section 3].…”

Section: Introductionmentioning

confidence: 99%

Ordered covering arrays and upper bounds on covering codes

Castoldi

Carmelo

Moura

et al. 2023

J of Combinatorial Designs

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“…al. [19], and Schaefer [22,24,23] n i distinct symbols, such that in every k-layer with n entries each symbol occurs exactly once and in any other k-layer with less entries each symbol occurs at most once. We write LHC(n 1 , ..., n d , k) for such an hypercuboid.…”

Section: Introductionmentioning

confidence: 99%

Endomorphisms of The Hamming Graph and Related Graphs

Schaefer

2016

Preprint

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In this paper we determine all singular endomorphisms of the Hamming graph and other related graphs. The Hamming graph has vertices Z m n where two vertices are adjacent, if their Hamming distance is 1. We show that its singular endomorphisms are uniform (each kernel has the same size) and that they are induced by Latin hypercubes (which essentially determines the number of singular endomorphisms). However, we do the same for its complement and some related graphs where the Hamming distance is allowed to be one of 1, ..., k, for some 1 ≤ k ≤ m − 1. Ultimately, we consider the same situation where the vertices are tuples in Zn 1 × Zn 2 × • • • × Zn m (not all ni are equal).

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“…. Readers might refer to recent work[17],[18],[19],[20],[21] for more information about such mathematical studies. There is also a…”

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confidence: 99%

A Survey of Constrained Combinatorial Testing

Wu¹,

Nie²,

Petke³

et al. 2019

Preprint

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Combinatorial Testing (CT) is a potentially powerful testing technique, whereas its failure revealing ability might be dramatically reduced if it fails to handle constraints in an adequate and efficient manner. To ensure the wider applicability of CT in the presence of constrained problem domains, large and diverse efforts have been invested towards the techniques and applications of constrained combinatorial testing. In this paper, we provide a comprehensive survey of representations, influences, and techniques that pertain to constraints in CT, covering 129 papers published between 1987 and 2018. This survey not only categorises the various constraint handling techniques, but also reviews comparatively less well-studied, yet potentially important, constraint identification and maintenance techniques. Since real-world programs are usually constrained, this survey can be of interest to researchers and practitioners who are looking to use and study constrained combinatorial testing techniques.

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Finite field constructions of combinatorial arrays

Cited by 9 publications

References 39 publications

Ordered covering arrays and upper bounds on covering codes

Ordered covering arrays and upper bounds on covering codes

Endomorphisms of The Hamming Graph and Related Graphs

A Survey of Constrained Combinatorial Testing

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