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Item type:Publication, Access status: with files , Dynamic programming in topological spaces(2020-10-23); ; Dynamic programming is a mathematical optimization method and a computer programming method as well. In this paper, the notion of sheaf programming in topological spaces is introduced and it is demonstrated that it relates very well to the concept of dynamic programming.Publicationtype: Preprint220 194 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Coding theory via Groebner basesCoding theory plays an important role in efficient transmission of data over noisy channels.In this thesis efficient encoding procedure for linear codes is developed using an algebraic approach. Description of linear codes as ideals in a residue class ring are given in terms of Groebner basis. While investigating primitive Reed Muller codes, a special family of linear codes with designed Hamming distance is obtained. A result proves their superiority over existing primitive Reed Muller codes. Furthermore, codes associated to a particular binomial ideal, defined as a sum of toric ideal and a prime ideal, are explored through minimal generators and Groebner basis. For these non-toric binomial ideals universal Groebner bases, Graver bases and circuits are also found. It is shown that each such binomial ideal has a natural reduced Groebner basis which provides a very compact encoding procedure. Finally, the binomial ideal of a linear code is presented in terms of its syzygy modules and the corresponding finite free resolution is also given.Publicationtype: Doctoral Thesis561 1118