Document Type
Article
Publication Date
11-2020
Abstract
We investigate how Legendre G-array pairs are related to several different perfect binary G-array families. In particular we study the relations between Legendre G-array pairs, Sidelnikov-Lempel-Cohn-Eastman ℤq−1-arrays, Yamada-Pott G-array pairs, Ding-Helleseth-Martinsen ℤ2×ℤmp-arrays, Yamada ℤ(q−1)/2-arrays, Szekeres ℤmp-array pairs, Paley ℤmp-array pairs, and Baumert ℤm1p1×ℤm2p2-array pairs. Our work also solves one of the two open problems posed in Ding~[J. Combin. Des. 16 (2008), 164-171]. Moreover, we provide several computer search based existence and non-existence results regarding Legendre ℤn-array pairs. Finally, by using cyclotomic cosets, we provide a previously unknown Legendre ℤ57-array pair.
Source Publication
Journal of Combinatorial Designs (ISSN 1063-8539 | e-ISSN 1520-6610)
Recommended Citation
Arasu, K. T., Bulutoglu, D. A., & Hollon, J. R. (2020). Legendre G-array pairs and the theoretical unification of several G-array families. Journal of Combinatorial Designs, 28(11), 814–841. https://doi.org/10.1002/jcd.21745
Comments
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The version of this article on AFIT Scholar is sourced from arXiv:2004.05608
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