Notes on Cyclic Convolutional Codes
Let Fq be the finite field of order q. We then denote by Fq[D] the set of polynomials in D with coefficients in Fq, and by Fq[D] the set of sequences on Fq:
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LECTURES - No. 219
INFORMATION THEORY NEW TRENDS AND OPEN PROBLEMS
EDITED BY
G. LONGO UNIVERSITY OF TRIESTE
SPRINGER-VERLAG WIEN GMBH
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concemed specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks.
© 1975 by Springer-Verlag Wien Originally published by Springer Verlag Wien-New York in 1975
ISBN 978-3-211-81378-2 DOI 10.1007/978-3-7091-2730-8
ISBN 978-3-7091-2730-8 (eBook)
CONTENTS Page Preface. PART ONE: FOUNDATIONS. H.W. Gattinger : Leetute Notes on Concepts and Measures of Information. . . . . . . . . . . . . . . G. Della Riccia: Self-Organizing Dynamics with Entropy Potentials F.J. Evans: Physics, Structure and Information. . . . . . . . . PART TWO : SHANNON THEORY. . . . . . . . M. Zakai, J. Ziv : A Generalization of the Rate-Distortion Theory and Applications. . . . . . . . . . . . . . . . . . J.K. Wolf: The AEP Property of Random Sequences and Applications to Information Theory Part I Basic Principles. . . . . . Part II : Single-User Communications. Part III : Multi-User Communications. J.K. Wolf: Constructive Codes for Multi-User Communication Channels . . . . . . . . . . . . . . . . ]. Körner : Same Methods in Multi-User Communication : A Tutorial Survey. . . . . . . . . . . . . . . . . . . . PART THREE : CODING THEORY. J.H. van Lint : Combinatorial Designs Constructed from or with Coding Theory. . . . . . . . . . . . . . . J.P.M. Schalkwijk: Symmetries of the State Diagram of the Syndrome Former of a Binaty Rate+ Convolutional Code Ph. Piret : Notes an Cyclic Convolutional Codes. . . . . P. Camion : Global Quadratic Abelian Codes. . . . . . . A. Huberman, A. Chouchan : Preparata Codes and Goethals' General-
III
1 3 45 61
85 87
125 139 14 7 15 7 173 225 227 263 283 293
Contents
II
ization : The Dual of a Nonlinear Code. . . . . . . . G.D. Cohen, S. Harari: Properties ofWeight Enumerator Polynomials. G.D. Cohen, P.J. Godlewski : Residual Error Rate of Binary Linear Block Codes. . . . . . . . . . . . . . . . . LIST OF CONTRIBUTORS. LIST OF PARTICIPANTS..
311 319 325 337 339
PREFACE
The birth of Information Theory is placed officially in 1948, when Claude E. Shannon published his first epoch-making paper on this subject. In spite of the enormaus importance and far-reaching consequences of this contribution, which turned Information Theory into a science, one should be aware of the constant presence, at least in Western philosophy, of a line of thought for which form, structure, relation and the like were more basic than matter, energy or substance. This line of thought, which goes back to the Pythagoreans, was mostly succumbing in front of the hold partisans of matter and energy, especially when matter and energy proved tobe exploitable for improving man's standard of life (besides having other less desirable but equally conspicuous uses). Quite recently, however, form
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