Szanowni Państwo,

 

Serdecznie zapraszamy na seminarium "Geometria i Układy Dynamiczne". Seminarium odbędzie się 15.06.2023 (czwartek), w godzinach 13:15-15:00 w sali A1/22.

 

Prelegent: Mariusz Kwiatkowski

 

Tytuł: O grafach kodów liniowych

 

Streszczenie: 

Linear $[n,k]_q$ codes are $k$-dimensional subspaces of an $n$-dimensional vector space over the field with $q$-elements. Non-degenerate codes are codes whose generating matrices contain no zero columns. Projective codes are codes whose every two columns of their generating matrices are non-proportional. In general codes whose every $t$ columns of their generating matrices are linearly independent are dual codes with minimal Hamming distance at least $t+1.$. The projective codes of maximal length are simplex codes.

 

Two distinct linear codes of any of those classes are adjacent vertices of the Grassmann graph if they have the maximal possible number of common codewords, i.e. the dimension of their intersection is $k-1$ dimensional. They induce subgraphs of the Grassmann graphs

We present overview of results regarding those subgraphs, including some general properties of those classes and a specific example of the graph of simplex $[5,2]_4$ codes.

 

Z poważaniem, 

A. Denisiuk, A. Doliwa, V. Shevchishin, A. Siemaszko