Families of Multidimensional Periodic Arrays with Large Peak Auto- to Cross-correlation Ratios

Families of Multidimensional Periodic Arrays with Large Peak Auto- to Cross-correlation Ratios | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 6 March 2026 V1 Latest version Share on Families of Multidimensional Periodic Arrays with Large Peak Auto- to Cross-correlation Ratios Authors : Cesar Bolaños Revelo 0009-0009-7361-6790 [email protected] and Dorothy Bollman Authors Info & Affiliations https://doi.org/10.22541/au.177279314.45589117/v1 138 views 63 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract reprint, amsmath,amssymb, aps, ]revtex4-2 We propose two new families of multidimensional periodic arrays for digital video watermarking. Starting from a Sidelnikov sequence x of length p l -1 having n-1 coprime factors m i we construct a base array by folding x into an (n-1)-dimensional periodic array. The two families are then obtained by composing the base array with a shift sequences defined by applying logarithmic quadratic and logarithmic fractional functions to a generation of the direct products of the additive groups Z m i . We show that both families exhibit peak auto-correlation on the order of p 2l , while non-peak auto-correlation and cross-correlation are on the order of p l for l ≥ n. Consequently, the proposed constructions achieve superior correlation ratios compared to existing methods and attain optimal low cross-correlation values with respect to the Welch bound. Supplementary Material File (cesarb_dorothyb_2026.pdf) Download 346.33 KB File (cesarb_dorothyb_2026.tex) Download 24.61 KB Information & Authors Information Version history V1 Version 1 06 March 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords array signal processing correlation theory galois fields sequences watermarking Authors Affiliations Cesar Bolaños Revelo 0009-0009-7361-6790 [email protected] University of Puerto Rico Mayaguez View all articles by this author Dorothy Bollman University of Puerto Rico Mayaguez View all articles by this author Metrics & Citations Metrics Article Usage 138 views 63 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Cesar Bolaños Revelo, Dorothy Bollman. Families of Multidimensional Periodic Arrays with Large Peak Auto- to Cross-correlation Ratios. Authorea . 06 March 2026. DOI: https://doi.org/10.22541/au.177279314.45589117/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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