Linear recurring sequences over finite fields

by McEliece, Robert James

Abstract (Summary)
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This thesis deals with the problem of how the elements from a finite field F of characteristic p are distributed among the various linear recurrent sequences with a given fixed characteristic polynomial [...]. The first main result is a method of extending the so-called "classical method" for solving linear recurrences in terms of the roots of f. The main difficulty is that f might have a root [...] which occurs with multiplicity exceeding p-1; this is overcome by replacing the solutions [...], [...], [...], ..., by the solutions [...], [...], [...], .... The other main result deals with the number N of times a given element [...] appears in a period of the sequence, and for [...], the result is of the form [...] where [...] is an integer which depends upon f, but not upon the particular sequence in question. Several applications of the main results are given.
Bibliographical Information:

Advisor:Marshall Hall

School:California Institute of Technology

School Location:USA - California

Source Type:Master's Thesis



Date of Publication:03/27/1967

© 2009 All Rights Reserved.