Basic algebra and combinatorics.

Aim of the course

To become familiar with the standard methods that are used to protect digital data, when they are transmitted (internet, infrared, wireless, etc.), as well as when they are stored on some information carrier (cd, dvd, magnetic tape, hard disc, etc). The data are to be protected against random errors caused by noise, damage, impurities, and so on. To show how one can apply these codes to a public key cryptosystem and secret sharing.

Topics to be discussed are:

  • Error correcting codes
  • q-ary symmetric channel and the probability of correct decoding
  • Systematic encoding, information sets and MDS codes
  • Weight enumerator of a code
  • Cyclic, Reed-Solomon, Goppa and Reed-Muller codes
  • Several decoding algorithms

If time permits we will survey the following topics (not part of the examination):

  • NP-hard problems in coding theory
  • Cryptographic systems of McEliece and Niederreiter

Rules about Homework / Exam

Written final exam (3 hours) for 70%

Written intermediate exam (1,5 hours) for 20%

Computer exercises at https://oncourse.tue.nl for 10%

Lecture Notes / Literature

Codes, Cryptology and Curves with Computer Algebra

by R. Pellikaan. X.-W. Wu, S Bulygin and R. Jurrius,

to be published by Cambridge University Press

Lecturer

R. Pellikaan (TUe)