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    Calculation of the static and dynamical correlation energy of pseudo-one-dimensional beryllium systems via a many-body expansion

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    Low-dimensional beryllium systems constitute interesting case studies for the test of correlation methods because of the importance of both static and dynamical correlation in the formation of the bond. Aiming to describe the whole dissociation curve of extended Be systems we chose to apply the method of increments (MoI) in its multireference (MR) formalism. However, in order to do so an insight into the wave function was necessary. Therefore we started by focusing on the description of small Be chains via standard quantum chemical methods and gave a brief analysis of the main characteristics of their wave functions. We then applied the MoI to larger beryllium systems, starting from the Be6 ring. First, the complete active space formalism (CAS-MoI) was employed and the results were used as reference for local MR calculations of the whole dissociation curve. Despite this approach is well established for the calculation of systems with limited multireference character, its application to the description of whole dissociation curves still requires further testing. After discussing the role of the basis set, the method was finally applied to larger rings and extrapolated to an infinite chain

    Linear Codes from Some 2-Designs

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    A classical method of constructing a linear code over \gf(q) with a tt-design is to use the incidence matrix of the tt-design as a generator matrix over \gf(q) of the code. This approach has been extensively investigated in the literature. In this paper, a different method of constructing linear codes using specific classes of 22-designs is studied, and linear codes with a few weights are obtained from almost difference sets, difference sets, and a type of 22-designs associated to semibent functions. Two families of the codes obtained in this paper are optimal. The linear codes presented in this paper have applications in secret sharing and authentication schemes, in addition to their applications in consumer electronics, communication and data storage systems. A coding-theory approach to the characterisation of highly nonlinear Boolean functions is presented
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