Linear recurring sequences over finite fields

Citation

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

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 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.

Thesis Files