Finite Fields : Theory, Applications and Algoritms.

Intro -- Contents -- Preface -- Computing composed products of polynomials -- Actions of linearized polynomials on the algebraic closure of a finite field -- On degree bounds for invariant rings of finite groups over finite fields -- Irreducible polynomials of given forms -- An application of Galois calculus to Fq[t] -- Composition behavior of sub-linearised polynomials over a finite field -- Kernels and defaults -- Global function fields with many rational places and their applications -- Traces of roots of unity over prime fields -- The Fermat curve in characteristic p -- Computing zeta functions over finite fields -- Cyclic alternant codes induced by an automorphism of a GRS code -- On Kerdock codes -- Permutation group of the q-ary image of some qm-ary cyclic codes -- The number of solutions to a system of equations and spectra of codes -- The LD probable prime test -- Carmichael numbers and Lucas tests -- On the state complexity of some long codes -- ID-based key distribution system over an elliptic curve -- Symmetric sets of curves and combinatorial arrays -- Weight functions and the extension theorem for linear codes over finite rings.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.