McEliece, Robert James (1967) Linear recurring sequences over finite fields. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-10012002-154611
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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 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.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Degree Grantor:||California Institute of Technology|
|Division:||Physics, Mathematics and Astronomy|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||27 March 1967|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||02 Oct 2002|
|Last Modified:||26 Dec 2012 03:03|
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