Download Coding, Cryptography and Combinatorics by Keqin Feng, Harald Niederreiter, Chaoping Xing PDF

By Keqin Feng, Harald Niederreiter, Chaoping Xing

ISBN-10: 3034896026

ISBN-13: 9783034896023

It has lengthy been well-known that there are interesting connections among cod­ ing idea, cryptology, and combinatorics. accordingly it appeared fascinating to us to prepare a convention that brings jointly specialists from those 3 components for a fruitful alternate of principles. We selected a venue within the Huang Shan (Yellow Mountain) quarter, some of the most scenic parts of China, as a way to give you the extra inducement of a pretty place. The convention was once deliberate for June 2003 with the professional identify Workshop on Coding, Cryptography and Combi­ natorics (CCC 2003). people who find themselves accustomed to occasions in East Asia within the first half 2003 can wager what occurred finally, particularly the convention needed to be cancelled within the curiosity of the well-being of the individuals. The SARS epidemic posed too severe a danger. on the time of the cancellation, the association of the convention was once at a sophisticated degree: all invited audio system have been chosen and all abstracts of contributed talks have been screened via this system committee. therefore, it was once de­ cided to name on all invited audio system and presenters of authorised contributed talks to publish their manuscripts for ebook within the current quantity. Altogether, 39 submissions have been obtained and subjected to a different around of refereeing. After care­ ful scrutiny, 28 papers have been accredited for publication.

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Kasami, H. Tokushige, T. Fujiwara, H. Yamamoto and S. Lin, "A recursive maximum likelihood decoding algorithm for some transitive invariant binary block codes," IEICE Trans. Fundamentals, vol. E81-A, pp. 1916-1924, Sept. 1998. [7J T. Koumoto, and T. Kasami, "Top-down recursive maximum likelihood decoding using ordered statistics information for half rate codes," Technical Report of IEICE, IT2002-29, The Institute of Electronics, Information and Communication Engineers, pp. 13-18, Japan, Sept. 2002.

4). Adaptive Recursive MLD Algorithm 35 In the original (bottom~up) RMLD, Ta-table whose entries are (v[D], L[D]) for every D E Ta is constructed for every index a. For a leaf section Ia where IIa I = I, PaC 5;;; {O, I} and saC = {O} (if the minimum distance of Cis 2 or greater), and therefore Ta-table = {(b, La (b)) : b is the best in PaC}. 2) as follows: for DE T a , v[D] = v[{DooDI : Db E Tab, (Do, Dd is an adjacent pair in D}], L[D] = min(L[Do] + L[D I]), where the minimum is taken over (Do, D I ) E the set of adjacent pairs in D.

N n _ ~I . n 9 Therefore, to construct good algebraic geometry codes, we seek curves X defined over IF whose number of IF-rational points, Nq(X), divided by its genus g(X) is large. In fact, we'll need a family of curves {Xd defined over IF such that the ratio Nq(Xi)lg(Xi ) is large as i approaches infinity. For this purpose, let Nq(g) denote the maximal possible number of IF-rational points on a curve of genus 9 defined over IF, and consider the quantity A(q) = lim sup Nq(g) g-+oo 9 first introduced by Ihara in 1981.

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