Title: Coding and Cryptography Author(s): T.W. Koerner Pages: 62 Publisher: Publication date: 1998 Language: English Format: PDF ISBN-10: ISBN-13: Description: Contents
1 What is an error correcting code?
2 Hamming's breakthrough
3 General considerations
4 Linear codes
5 Some general constructions
6 Polynomials and elds
7 Cyclic codes
8 Shift registers
9 A short homily on cryptography
10 Stream cyphers
11 Asymmetric systems
12 Commutative public key systems
13 Trapdoors and signatures
14 Further reading
15 First Sheet of Exercises
16 Second Sheet of Exercises
Transmitting messages across noisy channels is an important practical problem. Coding theory provides explicit ways of ensuring that messages remain legible even in the presence of errors. Cryptography on the other hand, makes sure that messages remain unreadable | except to the intended recipient. These complementary techniques turn out to have much in common mathematically.
The syllabus for the course is de ned by the Faculty Board Schedules (which are minimal for lecturing and maximal for examining). I should very much appreciate being told of any corrections or possible improvements and might even part with a small reward to the rst nder of particular errors. This document is written in LATEX2e and stored in the le labelled ~twk/IIA/Codes.tex on emu in (I hope) read permitted form.
These notes are based on notes taken in the course of the previous lecturer Dr Pinch. Most of their virtues are his, most of their vices mine. Although the course makes use of one or two results from probability theory and a few more from algebra it is possible
to follow the course successfully whilst taking these results on trust. There is a note on further reading at the end but [7] is a useful companion for the rst three quarters of the course (up to the end of section 8) and [9] for the remainder. Please note that vectors are
row vectors unless otherwise stated.
Title: Coding and Cryptography