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All different Steiner systems S(2, 4, 3) of order 2 and rank 2 − m − 1 + s over $$\mathbb{F}_2$$, where 0 ≤ s ≤ m − 1, are constructed. The number of different systems S(2, 4, 3) whose incident matrices are orthogonal to a fixed code is obtained. A connection between the number of different Steiner systems and of different Latin cubes is described. [ABSTRACT FROM AUTHOR]

The structure of all different Steiner triple systems S(2−1, 3, 2) of rank 2− m+2 over $\mathbb{F}_2 $ is described. This induces a natural recurrent method for constructing Steiner triple systems of any rank. In particular, the method gives all different such systems of order 2 − 1 and rank ≤ 2 − m + 2. The number of such different systems of order 2 − 1 and rank less than or equal to 2 − m + 2 which are orthogonal to a given code is found. It is shown that all different triple Steiner systems of order 2 − 1 and rank ≤ 2 − m + 2 are derivative and Hamming. Furthermore, all such triples are embedded in quadruple systems of the same rank and in perfect binary nonlinear codes of the same rank. [ABSTRACT FROM AUTHOR]

A letter to the editor is presented in response to the article "Steiner Triple Systems S(2m - 1, 3, 2) of Rank 2m -m + 1 over F2" published in a 2012 issue.

Steiner systems S(2 − 1, 3, 2) of rank 2 − m+1 over the field $$\mathbb{F}_2$$ are considered. A new recursive method for constructing Steiner triple systems of an arbitrary rank is proposed. The number of all Steiner systems of rank 2 − m+1 is obtained. Moreover, it is shown that all Steiner triple systems S(2 − 1, 3, 2) of rank r ≤ 2 − m+1 are derived, i.e., can be completed to Steiner quadruple systems S(2, 4, 3). It is also proved that all such Steiner triple systems are Hamming; i.e., any Steiner triple system S(2 − 1, 3, 2) of rank r ≤ 2 − m + 1 over the field $$\mathbb{F}_2$$ occurs as the set of words of weight 3 of a binary nonlinear perfect code of length 2−1. [ABSTRACT FROM AUTHOR]

For an arbitrary Steiner system S( v, k, t), we introduce the concept of a component as a subset of a system which can be transformed (changed by another subset) without losing the property for the resulting system to be a Steiner system S( v, k, t). Thus, a component allows one to build new Steiner systems with the same parameters as an initial system. For an arbitrary Steiner system S( v, k, k − 1), we provide two recursive construction methods for infinite families of components (for both a fixed and growing k). Examples of such components are considered for Steiner triple systems S( v, 3, 2) and Steiner quadruple systems S( v, 4, 3). For such systems and for a special type of so-called normal components, we find a necessary and sufficient condition for the 2-rank of a system (i.e., its rank over $\mathbb{F}_2$) to grow under switching of a component. It is proved that for k ≥ 5 arbitrary Steiner systems S( v, k, k − 1) and S( v, k, k − 2) have maximum possible 2-ranks. [ABSTRACT FROM AUTHOR]

Focuses on the design of a rapid single-flux-quantum switching cryonetwork for petaflops-scale computing. Backpressure and buffering; Throughput and latency of banyan and mesh networks; Modeling and simulation results.

Objective: The current study longitudinally examines college student Twitter patterns throughout initial phases of the COVID-19 pandemic. This study aims to better understand psychological impact and online personal communication during the pandemic., Participants: A dataset consisting of ∼720,000 tweets posted by students from universities throughout the United States during the 2020 spring semester was analyzed according to structural and sentimental analysis., Methods: Using a data-driven approach, three time periods emerged which reflected the transition to online learning., Results: Significant changes in structure and sentiment of tweets were observed across phases., Conclusions: Changes in Twitter patterns revealed important features of this unprecedented transition to online learning for college students.