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Item type:Publication, Access status: without files , On the Decomposition of Generalized SemiautomataSemiautomata are abstractions of electronic devices that are deterministic finite-state machines having inputs but no outputs. Generalized semiautomata are obtained from stochastic semiautomata by dropping the restrictions imposed by probability. It is well-known that each stochastic semiautomaton can be decomposed into a sequential product of a dependent source and deterministic semiautomaton making partly use of the celebrated theorem of Birkhoff-von Neumann. It will be shown that each generalized semiautomaton can be partitioned into a sequential product of a generalized dependent source and a deterministic semiautomaton.Publicationtype: Journal Article34 - Some of the metrics are blocked by yourconsent settings
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 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Groebner bases for linear codes over GF(4)A linear code over a prime field can be described by a binomial ideal in a polynomial ring given as the sum of a toric ideal and a nonprime ideal. A Groebner basis for such an ideal can be read off from a systematic generator matrix of the corresponding code. In this paper, a similar result will be presented for linear codes over GF(4). To this end, the extented alphabet GF(4) is dealt with by enlarging the polynomial ring. © 2011 Academic Publications, Ltd.Publicationtype: Journal Article14 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Groebner bases for quaternary codesA linear code can be described by a binomial ideal in a polynomial ring, given as the sum of a toric ideal and a nonprime ideal. A Groebner basis for such an ideal can be read off from a systematic generator matrix for the corresponding code. In this paper, an analogue result will be presented for quaternary codes. © 2011 Academic Publications, Ltd.Publicationtype: Journal Article10