عنوان

Coding Theory and Number Theory

شابک

9789048162574

شابک

9789401703055

شماره

b408459

عنوان اصلي

Coding Theory and Number Theory

نام عام مواد

[Book]

نام نخستين پديدآور

by Toyokazu Hiramatsu, Günter Köhler.

محل نشرو پخش و غیره

Dordrecht :

نام ناشر، پخش کننده و غيره

Imprint: Springer,

تاریخ نشرو بخش و غیره

2003.

عنوان فروست

Mathematics and Its Applications ;

مشخصه جلد

554-A

متن يادداشت

1. Linear Codes -- 2. Diophantine Equations and Cyclic Codes -- 3. Elliptic Curves, Hecke Operators and Weight Distribution of Codes -- 4. Algebraic-Geometric Codes and Modular Curve Codes -- 5. Theta Functions and Self-Dual Codes -- The Kloosterman Codes and Distribution of the Weights -- 1 Introduction -- 2 Melas code and Kloosterman sums -- 3 Hyper-Kloosterman code -- 4 Quasi-cyclic property -- 5 Weight distribution -- 7 A divisibility theorem for Hamming weights -- References.

بدون عنوان

0

متن يادداشت

This book grew out of our lectures given in the Oberseminar on 'Cod ing Theory and Number Theory' at the Mathematics Institute of the Wiirzburg University in the Summer Semester, 2001. The coding the ory combines mathematical elegance and some engineering problems to an unusual degree. The major advantage of studying coding theory is the beauty of this particular combination of mathematics and engineering. In this book we wish to introduce some practical problems to the math ematician and to address these as an essential part of the development of modern number theory. The book consists of five chapters and an appendix. Chapter 1 may mostly be dropped from an introductory course of linear codes. In Chap ter 2 we discuss some relations between the number of solutions of a diagonal equation over finite fields and the weight distribution of cyclic codes. Chapter 3 begins by reviewing some basic facts from elliptic curves over finite fields and modular forms, and shows that the weight distribution of the Melas codes is represented by means of the trace of the Hecke operators acting on the space of cusp forms. Chapter 4 is a systematic study of the algebraic-geometric codes. For a long time, the study of algebraic curves over finite fields was the province of pure mathematicians. In the period 1977 - 1982, V. D. Goppa discovered an amazing connection between the theory of algebraic curves over fi nite fields and the theory of q-ary codes.

شماره استاندارد بين المللي کتاب و موسيقي

9789048162574

عنوان

Springer eBooks

موضوع مستند نشده

Coding theory.

موضوع مستند نشده

Computational complexity.

موضوع مستند نشده

Computer science.

موضوع مستند نشده

Geometry, Algebraic.

موضوع مستند نشده

Matrix theory.

موضوع مستند نشده

Number theory.

مستند نام اشخاص تاييد نشده

Hiramatsu, Toyokazu.

مستند نام اشخاص تاييد نشده

Köhler, Günter.

مستند نام تنالگان تاييد نشده

SpringerLink (Online service)

تاريخ عمليات

20190301075700.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y