Bent Functions Fundamentals and Results
This book gives a detailed survey of the main results on bent functions over finite fields, presents a systematic overview of their generalizations, variations and applications, considers open problems in classification and systematization of bent functio
- PDF / 6,730,047 Bytes
- 561 Pages / 439.42 x 683.15 pts Page_size
- 29 Downloads / 255 Views
Bent Functions Fundamentals and Results
Bent Functions
Sihem Mesnager
Bent Functions Fundamentals and Results
123
Sihem Mesnager University of Paris VIII Paris, France
ISBN 978-3-319-32593-4 DOI 10.1007/978-3-319-32595-8
ISBN 978-3-319-32595-8 (eBook)
Library of Congress Control Number: 2016942544 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
In everyone’s life, at some time, our inner fire goes out. It is then burst into flame by an encounter with another human being. We should all be thankful for those people who rekindle the inner spirit. — Albert Schweitzer
To my husband Laurent
List of Symbols and Notation
General #S Cardinality of the set S . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . viii C Field of complex numbers . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . viii F2n Finite field with 2n elements . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . viii Fq Finite field with q elements . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . viii N Semiring of non-negative integers .. . . . . . . . .. . . . . . . . . . . . . . . . . . . . . viii R Field of real numbers .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . viii Z Ring of integers .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . viii K An algebraic closure of K . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . viii K; L A perfect field or a number field . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . viii l A prime number different from p .. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . viii p A prime number . . . . . . . . . . . .
Data Loading...
