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Linear Recurring Sequences Over Finite Fields


McEliece, Robert James (1967) Linear Recurring Sequences Over Finite Fields. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1KMK-T118.


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 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 θ which occurs with multiplicity exceeding p-1; this is overcome by replacing the solutions θt, tθt, t2θt, ..., by the solutions θt, (t1t, (t2t, .... 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 pε 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):
  • Hall, Marshall
Thesis Committee:
  • Unknown, Unknown
Defense Date:27 March 1967
Funding AgencyGrant Number
Record Number:CaltechETD:etd-10012002-154611
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3856
Deposited By: Imported from ETD-db
Deposited On:02 Oct 2002
Last Modified:19 Mar 2024 21:08

Thesis Files

PDF (McEliece_rj_1967.pdf) - Final Version
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