The Department of Mathematical Foudations of Informatics
is generally concerned with research, implementation and education in the
field of coding theory, cryptography, combinatorics and computer algebra.
The major research efforts are currently focused
on the following areas.
-
Optimal codes:
determining exact values or improving the known bounds for nq(n,d)
and dq(n,k),
characterization of codes with given parameters
( Dodunekov ,
Manev ,
Landjev,
Boukliev ,
Kolev,
Bogdanova ,
Vavrek ).
-
Covering problems:
covering radius and football-pool problems
( Dodunekov ,
Kolev,
Baicheva ).
-
Codes and designs in polynomial spaces:
linear programming bounds, optimal codes and designs
( Dodunekov,
Boyvalenkov,
Kazakov,
Boumova ).
-
q-ary images of codes over GF(qm)-codes
( Manev ,
Kolev ).
-
MDS and near-MDS codes
( Dodunekov ,
Landjev ).
-
Decoding algorithms
( Dodunekov ,
Manev,
Landjev ).
-
Error correcting codes in cryptography
minimal codewords, identification, sharing schemes
( Manev,
Landjev,
Nikolov ).
-
Codes and designs, finite geometries
( Landjev ,
Boyvalenkov ,
Topalova ).
-
Computer algebra:
Computational Group Theory and developing a system for calculations in/over
finite fields (GFQ)
( Bogdanova ,
Topalova ,
Boukliev ,
Baicheva ,
Kazakov ,
Vavrek ).
-
Performance of linear block codes used for error detection/correction
( Baicheva ,
Dodunekov ,
Kazakov )
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