Algebraic Coding: First French-Israeli Workshop Paris, by V. B. Balakirsky (auth.), G. Cohen, S. Litsyn, A. Lobstein,

By V. B. Balakirsky (auth.), G. Cohen, S. Litsyn, A. Lobstein, G. Zémor (eds.)

This quantity offers the lawsuits of the 1st French-Israeli Workshop on Algebraic Coding, which came about in Paris in July 1993. The workshop was once a continuation of a French-Soviet Workshop held in 1991 and edited through a similar board. The completely refereed papers during this quantity are grouped into components on: convolutional codes and precise channels, protecting codes, cryptography, sequences, graphs and codes, sphere packings and lattices, and boundaries for codes.

Show description

Read Online or Download Algebraic Coding: First French-Israeli Workshop Paris, France, July 19–21, 1993 Proceedings PDF

Similar algebra books

Polynomes, etude algebrique

Les polynômes permettent de résumer les calculs de base sur les nombres : somme, produit, élévation à une puissance entière. C'est los angeles raison pour laquelle ils se sont si tôt introduits comme outils naturels des mathématiques. Formellement, ils sont utilisés comme des schémas universels pour ces calculs, puisque, par substitution, ils permettent de réaliser tout calcul concret à partir de manipulation abstraite.

Zahlentheorie: Eine Einführung in die Algebra

Auf der Grundlage der Mathematikkenntnisse des ersten Studienjahres bietet der Autor eine Einführung in die Zahlentheorie mit Schwerpunkt auf der elementaren und algebraischen Zahlentheorie. Da er die benötigten algebraischen Hilfsmittel nicht voraussetzt, sondern everlasting mitentwickelt, wendet sich das Buch auch an Nichtspezialisten, denen es über die Zahlen frühzeitig den Weg in die Algebra öffnet.

Additional resources for Algebraic Coding: First French-Israeli Workshop Paris, France, July 19–21, 1993 Proceedings

Sample text

Xiii) False. 0 0 is a counter-example. (xiv) False. For example, 1 [0 0 1 0][1 0]- [0 1 4][0 0] (xv) True. (xvi) True. (xvii) False. Take, for example, f, g : IR" -* IR' given by f (x, y) (0, 0) and g(x, y) = (x, y). Relative to the standard basis of IR' we see Linear algebra Book 4 that f is represented by the zero matrix and g is represented by the identity matrix; and there is no invertible matrix P such that P-142P = 0. (xviii) True. (xix) False. The transformation t is non-singular (an isomorphism), but r1 21 1 2J is singular.

Prove that (1) if det A = 1 and n is odd, or if det A = -1 and n is even, then 1 is an eigenvalue of A; (2) if det A = -1 then -1 is an eigenvalue of A. 28 If A is a skew-symmetric matrix and g(X) is a polynomial such that g(A) = 0, prove that g(-A) = 0. Deduce that the minimum polynomial of A contains only terms of even degree. Deduce that if A is skew-symmetric and f (X), g(X) are polynomials whose terms are respectively odd and even then f (A), g(A) are respectively skew-symmetric and symmetric.

V = Ker t ® Im t holds in cases (i) and (ii), but not in case (iii); for in case (iii) we have that (1, 1, 1) belongs to both Kert and Imt. 4 If s o t = idv then s is surjective, hence bijective (since V is of finite dimension). Then t = s-1 and so t o s = idv. Suppose that W is t-invariant, so that t(W) C_ W. Since t is an isomorphism we must have dimt(W) = dim W and so t(W) = W. Hence W = s[t(W)] = s(W) and W is s-invariant. The result is false for infinite-dimensional spaces. For example, consider the real vector space IR[X] of polynomials over IR.

Download PDF sample

Rated 4.34 of 5 – based on 47 votes