Download Algebraic Function Fields and Codes by Henning Stichtenoth PDF

By Henning Stichtenoth

The concept of algebraic functionality fields has its origins in quantity conception, advanced research (compact Riemann surfaces), and algebraic geometry. given that approximately 1980, functionality fields have stumbled on extraordinary purposes in different branches of arithmetic similar to coding idea, cryptography, sphere packings and others. the most goal of this publication is to supply a in simple terms algebraic, self-contained and in-depth exposition of the speculation of functionality fields.

This new version, released within the sequence Graduate Texts in arithmetic, has been significantly improved. furthermore, the current version comprises a number of routines. a few of them are really effortless and aid the reader to appreciate the elemental fabric. different workouts are extra complex and canopy extra fabric that may now not be incorporated within the text.

This quantity is especially addressed to graduate scholars in arithmetic and theoretical laptop technology, cryptography, coding idea and electric engineering.

Show description

Read Online or Download Algebraic Function Fields and Codes PDF

Similar cryptography books

Beginning Cryptography with Java

Whereas cryptography can nonetheless be a debatable subject within the programming group, Java has weathered that hurricane and offers a wealthy set of APIs that let you, the developer, to successfully comprise cryptography in applications-if you recognize how.

This e-book teaches you ways. Chapters one via 5 disguise the structure of the JCE and JCA, symmetric and uneven key encryption in Java, message authentication codes, and the way to create Java implementations with the API supplied by means of the Bouncy citadel ASN. 1 applications, all with lots of examples. construction on that beginning, the second one half the publication takes you into higher-level themes, permitting you to create and enforce safe Java purposes and utilize typical protocols corresponding to CMS, SSL, and S/MIME.

What you are going to examine from this ebook the best way to comprehend and use JCE, JCA, and the JSSE for encryption and authentication The ways that padding mechanisms paintings in ciphers and the way to identify and fasten standard mistakes An realizing of ways authentication mechanisms are applied in Java and why they're used tools for describing cryptographic gadgets with ASN. 1 how you can create certificates revocation lists and use the web certificates prestige Protocol (OCSP) Real-world internet suggestions utilizing Bouncy citadel APIs

Who this e-book is for

This ebook is for Java builders who are looking to use cryptography of their purposes or to appreciate how cryptography is getting used in Java functions. wisdom of the Java language is critical, yet you needn't be accustomed to any of the APIs discussed.

Wrox starting publications are crafted to make studying programming languages and applied sciences more uncomplicated than you're thinking that, offering a established, instructional layout that might consultant you thru the entire options concerned.

Web and Information Security

Edited models of chosen papers from a 2002 IEEE COMPSAC workshop held in Oxford, united kingdom, including numerous extra papers on nation- of-the-art themes, conceal key advancements, instructions, and demanding situations for securing the semantic net, handling and imposing protection rules, and securing rising platforms similar to multimedia and collaborative networks.

Robust Computer Vision: Theory and Applications (Computational Imaging and Vision)

From the foreword by means of Thomas Huang: "During the earlier decade, researchers in desktop imaginative and prescient have came upon that probabilistic computing device studying tools are super strong. This e-book describes a few of these equipment. as well as the utmost chance framework, Bayesian Networks, and Hidden Markov types also are used.

Open Source Software for Digital Forensics

Open resource ApplicationsSpringer ebook SeriesEditor: Ernesto Damiani, college of Milan, Italyhttp://sesar. dti. unimi. it/ossbook/Open resource software program for electronic Forensics is the 1st publication devoted to using FLOSS (Free Libre Open resource software program) in desktop forensics. It provides the motivations for utilizing FLOSS functions as instruments for assortment, maintenance and research of electronic facts in desktop and community forensics.

Extra info for Algebraic Function Fields and Codes

Example text

Let P ∈ IPF . An integer n ≥ 0 is called a pole number of P if there is an element x ∈ F with (x)∞ = nP . Otherwise n is called a gap number of P . Clearly n is a pole number of P if and only if (nP ) > ((n − 1)P ). Moreover, the set of pole numbers of P is a sub-semigroup of the additive semigroup IN (to see this note that, if (x1 )∞ = n1 P and (x2 )∞ = n2 P then x1 x2 has the pole divisor (x1 x2 )∞ = (n1 + n2 )P ). 8 (Weierstrass Gap Theorem). Suppose that F/K has genus g > 0 and P is a place of degree one.

Pin−d )) = deg G − n + d . Hence d ≥ n − deg G. 3. Suppose that the degree of G is strictly less than n. Then the evaluation map evD : L (G) → CL (D, G) is injective, and we have: 50 2 Algebraic Geometry Codes (a) CL (D, G) is an [n, k, d] code with d ≥ n − deg G and k = (G) ≥ deg G + 1 − g . Hence k+d ≥ n+1−g. 5) (b) If in addition 2g − 2 < deg G < n, then k = deg G + 1 − g. (c) If {x1 , . . , xk } is a basis of L (G) then the matrix ⎛ ⎞ x1 (P1 ) x1 (P2 ) . . x1 (Pn ) ⎜ ⎟ .. .. M =⎝ ⎠ . .

Then there is an element 0 = x ∈ L (G) such that the codeword (x(P1 ), . . , x(Pn )) ∈ CL (D, G)) has precisely n − d = n − d∗ = deg G zero components, say x(Pij ) = 0 for j = 1, . . , deg G. Put deg G D := Pij . j=1 Then 0 ≤ D ≤ D, deg D = deg G and (G − D ) > 0 (as x ∈ L (G − D )). Conversely, if D has the above properties then we choose an element 0 = y ∈ L (G − D ). The weight of the corresponding codeword (y(P1 ), . . , y(Pn )) is n − deg G = d∗ , hence d = d∗ . Another code can be associated with the divisors G and D, by using local components of Weil differentials.

Download PDF sample

Rated 4.10 of 5 – based on 34 votes