Essays about: "Galois Fields"

Showing result 1 - 5 of 6 essays containing the words Galois Fields.

  1. 1. The Abel-Ruffini Theorem : The insolvability of the general quintic equation by radicals

    University essay from Umeå universitet/Institutionen för matematik och matematisk statistik

    Author : Axel Sjöblom; [2024]
    Keywords : ;

    Abstract : This thesis explores the topic of Galois theory at a relatively introductory level with the goal of proving the Abel Ruffini theorem. In the first part algebraic structures are considered: groups, ring, fields, etc. Following this, polynomial rings are introduced and the attention is then turned to finite field-extensions. READ MORE

  3. 2. The low-lying zeros of L-functions associated to non-Galois cubic fields

    University essay from Göteborgs universitet/Institutionen för matematiska vetenskaper

    Author : Victor Ahlquist; [2023-02-13]
    Keywords : Mathematics; number theory; cubic fields; L-functions; low-lying zeros; onelevel density; two-level density; phase transition.;

    Abstract : We study the low-lying zeros of Artin L-functions associated to non-Galois cubic number fields through their one- and two-level densities. In particular, we find new precise estimates for the two-level density with a power-saving error term. READ MORE

  4. 3. Profinite groups

    University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Juan Moreno Poncela; [2023]
    Keywords : Profinite Groups; Infinite Galois Theory; Mathematics and Statistics;

    Abstract : This thesis provides a comprehensive study of profinite groups, which are fascinating mathematical objects that have attracted significant interest in modern algebraic research. Profinite groups are infinite generalizations of finite groups and share many similarities with them. READ MORE

  5. 4. Construction of Superimposed Codes Using Graphs and Galois Fields

    University essay from Karlstads universitet/Institutionen för matematik och datavetenskap (from 2013)

    Author : David Johansson; [2017]
    Keywords : ;

    Abstract : In this thesis some constructions of superimposed codes are presented. Many of the known nontrivial constructions arise from t−designs, and the constructions discussed in this thesis is also based on a block design idea. Superimposed codes are rather combinatorial in nature, so the connection to t−designs is not too surprising. READ MORE

  6. 5. Efficient Message Passing Decoding Using Vector-based Messages

    University essay from Institutionen för systemteknik

    Author : Mikael Grimnell; Mats Tjäder; [2005]
    Keywords : Forward Error Correction; Low Density Parity Check Codes; Message Passing Decoding; Belief Propagation; Extrinsic Information Transfer; Galois Fields; Phase Shift Keying;

    Abstract : The family of Low Density Parity Check (LDPC) codes is a strong candidate to be used as Forward Error Correction (FEC) in future communication systems due to its strong error correction capability. Most LDPC decoders use the Message Passing algorithm for decoding, which is an iterative algorithm that passes messages between its variable nodes and check nodes. READ MORE