Citation
McEliece, Robert James (1967) Linear Recurring Sequences Over Finite Fields. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1KMKT118. https://resolver.caltech.edu/CaltechETD:etd10012002154611
Abstract
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 fε F[x]. 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 θ which occurs with multiplicity exceeding p1; this is overcome by replacing the solutions θ^{t}, tθ^{t}, t^{2}θ^{t}, ..., by the solutions θ^{t}, (t_{1})θ^{t}, (t_{2})θ^{t}, .... The other main result deals with the number N of times a given element a ε F appears in a period of the sequence, and for a≠0, the result is of the form N≡0 (mod p^{ε} where ε 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.))  

Subject Keywords:  (Mathematics)  
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  
Funders: 
 
Record Number:  CaltechETD:etd10012002154611  
Persistent URL:  https://resolver.caltech.edu/CaltechETD:etd10012002154611  
DOI:  10.7907/1KMKT118  
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:  19 Mar 2024 21:08 
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