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We employ algebraic methods to provide some new constructions of what we call optimal high-energy ternary sequences (a sequence with entries in {0, 1, −1} with a single zero, having optimal correlation properties). Our motivation for these constructions stems from their usefulness in several areas related to communication and radar systems.

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 Z q − 1‐arrays, Yamada‐Pott G‐array pairs, Ding‐Helleseth‐Martinsen Z 2 × Z p m‐arrays, Yamada Z ( q − 1 ) ∕ 2‐arrays, Szekeres Z p m‐array pairs, Paley Z p m‐array pairs, and Baumert Z p 1 m 1 × Z p 2 m 2‐array pairs. Our work also solves one of the two open problems posed by Ding. Moreover, we provide several computer search‐based existence and nonexistence results regarding Legendre Z n‐array pairs. Finally, by using cyclotomic cosets, we provide a previously unknown Legendre Z 57‐array pair.

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Although direct measurements of the projected areas of various Geosynchronous Earth Orbit (GEO) satellite facets are impossible without high-resolution imaging, estimates of the albedo-Area (aA) product lead to the possibility of inferring the geometric size of an RSO based on the illuminated area. Such size estimates are an integral part of its identity because satellite mission capabilities can be inferred. We are engaged in parallel development of two methods for calculating aA for the body/communication antennas structures and one method for the solar panels. We have previously reported on the Two Facet Model (2FM) method for body aA, and here we discuss a method based on differences between new observations and a baseline catalog that has been constructed from the GEO Observations with Longitudinal Diversity Simultaneously (GOLDS) data. We report on evaluations of the 2FM and Differential Method (DM) algorithm results. We also discuss a new method of estimating solar panel aA by fitting new data that include specular glints. All of these measurement methods are compared to models and simulations that serve as a proxy for ground truth. Because of the partially directional nature of the composite Bi-directional Reflectivity Distribution Function (BRDF) of all bus-mounted appendages, variance of body aA results is expected to be significant. Short-term and long-term variance of the derived aAs will also be discussed.