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Spectra of weighted networks have received increasing attention from scientific community, such as mathematical chemistry, computer science, coding theory. The real networks behavior is completely differently, not only in the degree distribution, but also in the weight distribution. In this paper, we determine the generalized adjacency (resp., Laplacian and signless Laplacian) spectra of the weighted neighbourhood corona networks with different structures. As applications, the two important indices of the weighted neighbourhood corona networks are computed. [ABSTRACT FROM AUTHOR]

Such sections of algebra as the theory of finite fields and the theory of polynomials over finite fields have increasingly influence on the construction of various systems for protecting information, encoding and decoding information. In the last two decades, polynomials, especially irreducible polynomials, have played a significant role in computer cryptography. Using the properties of irreducible polynomials maximizes the efficient computer implementation of arithmetic in finite fields, which is of particular importance for cryptography and coding theory. The present paper is devoted to the study of irreducible polynomials of a special type. Namely, explicit root polynomial formulas for third-degree cyclic polynomials over a field of characteristic 2 are obtained. A review of known results on irreducible normal polynomials and sets of their root polynomials over arbitrary fields is also given. In addition, the problem of finding irreducible polynomials is considered. The results of the work can be used in cryptographic applications and coding theory. [ABSTRACT FROM AUTHOR]