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In this paper, we observe simple yet subtle interconnections among design theory, coding theory and cryptography. Maximum distance separable (MDS) matrices have applications not only in coding theory but are also of great importance in the design of block ciphers and hash functions. It is nontrivial to find MDS matrices which could be used in lightweight cryptography. In the SAC 2004 paper [12], Junod and Vaudenay considered bi-regular matrices which are useful objects to build MDS matrices. Bi-regular matrices are those matrices all of whose entries are nonzero and all of whose 2×2{2\times 2} submatrices are nonsingular. Therefore MDS matrices are bi-regular matrices, but the converse is not true. They proposed the constructions of efficient MDS matrices by studying the two major aspects of a d×d{d\times d} bi-regular matrix M, namely v1⁢(M){v_{1}(M)}, i.e. the number of occurrences of 1 in M, and c1⁢(M){c_{1}(M)}, i.e. the number of distinct elements in M other than 1. They calculated the maximum number of ones that can occur in a d×d{d\times d} bi-regular matrices, i.e. v1d,d{v_{1}^{d,d}} for d up to 8, but with their approach, finding v1d,d{v_{1}^{d,d}} for d≥9{d\geq 9} seems difficult.

Reptarenaviruses cause Boid Inclusion Body Disease (BIBD), and co-infections by several reptarenaviruses are common in affected snakes. Reptarenaviruses have only been found in captive snakes, and their reservoir hosts remain unknown. In affected animals, reptarenaviruses appear to replicate in most cell types, but their complete host range, as well as tissue and cell tropism are unknown. As with other enveloped viruses, the glycoproteins (GPs) present on the virion’s surface mediate reptarenavirus cell entry, and therefore, the GPs play a critical role in the virus cell and tissue tropism. Herein, we employed single cycle replication, GP deficient, recombinant vesicular stomatitis virus (VSV) expressing the enhanced green fluorescent protein (scrVSV∆G-eGFP) pseudotyped with different reptarenavirus GPs to study the virus cell tropism. We found that scrVSV∆G-eGFPs pseudotyped with reptarenavirus GPs readily entered mammalian cell lines, and some mammalian cell lines exhibited higher, compared to snake cell lines, susceptibility to reptarenavirus GP-mediated infection. Mammarenavirus GPs used as controls also mediated efficient entry into several snake cell lines. Our results confirm an important role of the virus surface GP in reptarenavirus cell tropism and that mamma-and reptarenaviruses exhibit high cross-species transmission potential.

polygons, are useful in survey sampling in terms of balanced sampling plans excluding contiguous units (BSECs) and balanced sampling plans excluding adjacent units (BSAs) when neighboring units in a population provide similar information. In this paper, themethod of cyclic shifts is used and cyclic polygonal designs (CPDs) are constructed with block size k  3 and   1, 2, 3, 4, 6,12 for joint distance   3 and v{21, 22, ,100}treatments.