Citation
McEliece, Robert James (1967) Linear recurring sequences over finite fields. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd10012002154611
Abstract
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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 socalled "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 p1; 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.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  27 March 1967 
Record Number:  CaltechETD:etd10012002154611 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd10012002154611 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  3856 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  02 Oct 2002 
Last Modified:  26 Dec 2012 03:03 
Thesis Files

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