عنوان
پدید آورنده
موضوع
رده
کتابخانه
محل استقرار
NATIONAL BIBLIOGRAPHY NUMBER
Number
TL53039
LANGUAGE OF THE ITEM
.Language of Text, Soundtrack etc
انگلیسی
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Value Distribution of Elementary Symmetric Polynomials and Their Perturbations Over Finite Fields
General Material Designation
[Thesis]
First Statement of Responsibility
Rapello, César A. Serna
Subsequent Statement of Responsibility
Medina, Luis A.
.PUBLICATION, DISTRIBUTION, ETC
Name of Publisher, Distributor, etc.
University of Puerto Rico, Rio Piedras (Puerto Rico)
Date of Publication, Distribution, etc.
2020
GENERAL NOTES
Text of Note
62 p.
DISSERTATION (THESIS) NOTE
Dissertation or thesis details and type of degree
Ph.D.
Body granting the degree
University of Puerto Rico, Rio Piedras (Puerto Rico)
Text preceding or following the note
2020
SUMMARY OR ABSTRACT
Text of Note
In this work we present two studies related to exponential sums and Walsh transformations of q-ary functions. In our first study we establish the asymptotic behavior of some generating functions related to the exponential sum over finite fields of elementary symmetric functions and their perturbations. This asymptotic behavior allows us to calculate the probability generating function of the probability that the elementary symmetric polynomial of degree k (and its perturbations) returns β∈ Fq where Fq represents the field of q elements. Our study extends many of the results known for perturbations over the binary field to any finite field. In particular, we establish when a particular perturbation is asymptotically balanced over a prime field and provide a construction to find such perturbations over any finite field. Our second study is related to generalized p-ary functions. In particular, we show that Walsh-Hadamard transformations of generalized p-ary functions whose components are symmetric, rotation symmetric or a combination or concatenation of them are C-finite sequences. This result generalizes many of the known results for regular p-ary functions. We also present a study of the roots of the characteristic polynomials related to these sequences and show that properties like balancedness and being bent are not shared by the underline p-ary functions.
UNCONTROLLED SUBJECT TERMS
Subject Term
Applied mathematics
Subject Term
Mathematics
PERSONAL NAME - PRIMARY RESPONSIBILITY
Rapello, César A. Serna
PERSONAL NAME - SECONDARY RESPONSIBILITY
Medina, Luis A.
CORPORATE BODY NAME - SECONDARY RESPONSIBILITY
University of Puerto Rico, Rio Piedras (Puerto Rico)
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب p
[Thesis]
276903
a
Y
