Кафедра математической логики и теории алгоритмов

Lectures log 2016


Errors and erasures.
Code distance and its relation to the number of corrected errors and erasures.
Example: Hamming [n-1,n,2]-code.

The Volume bound. The Gilbert’s bound.
The formula for the volume of a Hamming ball. The Shannon function.
The Volume bound and the Gilbert bound for binary alphabet.


Linear codes.
A probabilistic proof of existence of linear codes on Gilbrt’s curve.

Wozencraft ensemble of codes.

Hamming [2^m-m-1,2^m-1]-code and [2^m-m,2^m]-code.

Singleton bound. Reed-Solomon codes.