**Prerequisites:**

- Linear algebra: matrices, Gaussian elimination, vector (sub)spaces, linear maps
- Algebra: groups, rings and ideals, (finite) fields
- Logic: logical inference and the structure of proofs
- Set theory and combinatorics: notation and properties of sets, counting

**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

Videos and slides of lectures: These lectures will be recorded on video and also the slides are available to participants through the following website: https://oncourse.tue.nl/2018/

and go to Mathematics and then to Coding Theory (2MMC30)

**Lecturer**

R. Pellikaan (TUe)

- Docent: Ruud Pellikaan