臺灣博碩士論文加值系統

一個geometric Goppa code是和決定它的因子息息相關的,在這份論文中,我們發現在某個條件下:兩個因子若是等價若且為若各自決定的geometric Goppa codes會等價。

A geometric Goppa code is associated with a divisor.
Under certain conditions, we prove that two geometric Goppa codes are equivalent
if and only if the associated divisors are equivalent.

Chapter 1. Introduction.................................1

Chapter 2. Basic Properties of Divisors and Weil Differentials...........................................3
2.1 Divisors.............................3
2.2 Weil Differentials.........................8

Chapter 3. Codes..............................13
3.1 Introduction to Codes...................13
3.2 Geometric Goppa Codes..................15

Chapter 4. Main Results.............................22
4.1 Equivalent Codes.............................22
4.2 Equality of Geometric Goppa Codes..............23
4.3 Equivalent Codes and Equivalent Divisors.....29

Bibligoraphy......................................32

Carlos Munuera and Ruud Pellikaan,
``Equality of geometric Goppa codes and equivalence of divisors,''
{\sl Journ. Pure Appl. Algebra,} vol. 90, pp. 229--252, 1993.
Henning Stichtenoth,
``Algebraic Function Field and Codes,'' Springer-Verlag, New York, 1993.
Judy L. Walker,
``Codes and curves,''Springer, 1999.
Chao-Ping, Xing,
``When are two geometric Goppa codes equal ?''
{\sl IEEE Transctions of information theory,} vol. 38, No. 3, May 1992.