Հայաստանի ատենախոսությունների բաց մատչելիության պահոց = Open Access Repository of the Armenian Electronic Theses and Dissertations (Armenian ETD-OA) = Репозиторий диссертаций Армении открытого доступа

Վերջավոր դաշտերի վրա անվերածելի և նորմալ բազմանդամների կառուցումներ

Մահմուդ, Ալիզադեհ (2013) Վերջավոր դաշտերի վրա անվերածելի և նորմալ բազմանդամների կառուցումներ. PhD thesis, ՀՀ ԳԱԱ ինֆորմատիկայի եվ ավտոմատացման պրոբլեմների ինստիտուտ.

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    Abstract

    The theory of finite fields is a branch of modern algebra that has come to the fore in the last 50 years because of its diverse application in combinatorics, coding theory, and mathematical study of switching circuits, among others. The origins of the subject reach back into the 17th and 18th century, with such eminent mathematicians as Pierre de Fermat(1601-1665), Leonhard Eular (1707-1738), Joseph-Louis Lagrange (1736-1813), and Adrien-Marie Legendre(1752-1833) contributing to the structure theory of special finite fields namely, the so-called finite prime fields. The general theory of finite fields may be said to begin with the work of Carl Friedrich Gauss (1777-1855) and Everiste Galois (1811-1832), but it only became of interest for applied mathematicians in recent decades with the emergence of discrete mathematics as a serious discipline. In parallel with the development of the theory of finite fields there was a rapid growth of polynomial theory based on finite fields. The finite fields based theory is important not only for the study of algebraic structures on finite fields, but it has many other applications, such as, coding theory and cryptography. Moreover, the irreducible and normal polynomials play a special role in this, as they are necessary in construction of finite fields and in procedures with the elements of the field. There are two methods for constructing irreducible (or normal) polynomials over finite fields. The first method is the polynomial composition method that allows constructions of irreducible (or normal) polynomials of higher degree from given irreducible (or normal) polynomials over finite fields. The second method is the testing method for irreducibility and normality of the polynomials over finite fields. The first method has been studied by Varshamov1, Cohen2, Kyuregyan3 and others. The second method has been studied by several authors, including Ben-Or4, Rabin5. The elements in a normal basis are exact roots of an

    Item Type: Thesis (PhD)
    Additional Information: Վերջավոր դաշտերի վրա անվերածելի և նորմալ բազմանդամների կառուցումներ: Построения непeреводимых, нормальных полиномов над конечными полями.
    Uncontrolled Keywords: Մահմուդ Ալիզադեհ, Махмуд Ализаде
    Subjects: Informatics and Computer Systems
    Divisions: UNSPECIFIED
    Depositing User: NLA Circ. Dpt.
    Date Deposited: 29 Sep 2016 17:27
    Last Modified: 04 Oct 2016 11:16
    URI: http://etd.asj-oa.am/id/eprint/3523

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