Citation
Erickson, Daniel Edwin (1974) Counting Zeros of Polynomials Over Finite Fields. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Q28MM322. https://resolver.caltech.edu/CaltechETD:etd10132005082129
Abstract
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The main results of this dissertation are described in the following theorem: Theorem 5.1 If P is a polynomial of degree r = s(q1) + t, with 0 < t <= q  1, in m variables over GF(q), and N(P) is the number of zeros of P, then: 1) N(P) > [...] implies that P is zero. 2) N(P) < [...] implies that N(P) [...] where [...] where (qt+3) [...] ct [...] t  1. Furthermore, there exists a polynomial Q in m variables over GF(q) of degree r such that N(Q) = [...]. In the parlance of Coding Theory 5.1 states: Theorem 5.1 The nexttominimum weight of the rth order Generalized ReedMuller Code of length [...] is (qt)[...] + [...] where c, s, and t are defined above. Chapter 4 deals with blocking sets of order n in finite planes. An attempt is made to find the minimum size for such sets.
Item Type:  Thesis (Dissertation (Ph.D.)) 

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

Thesis Committee: 

Defense Date:  20 September 1973 
Record Number:  CaltechETD:etd10132005082129 
Persistent URL:  https://resolver.caltech.edu/CaltechETD:etd10132005082129 
DOI:  10.7907/Q28MM322 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  4061 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  14 Oct 2005 
Last Modified:  24 Jul 2024 19:46 
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