I am interested in the theory of perfect codes. I have suggested several constructions of perfect codes by concatenation and switching (jointly with S. V. Avgustinovich). The following nontrivial properties of perfect binary codes are investigated. It was suggested the method of $\alpha$-components to construct perfect codes, the class of nonsystematic perfect codes was discovered jointly with S. V. Avgustinovich. The automorphism group of perfect codes; the metrical rigidity of $q$-ary codes close to perfect codes by close-packed properties; rank-kernel problem for perfect codes are investigated (jointly with different coworkers).
Main publications:
Solov'eva F. I. Switchings and perfect codes // Numbers, information and complexity. Dordrecht: Kluwer Acad. Publ., 2000, 311–314.
Solov'eva F. I. Structure of $i$-components of perfect binary codes, Discrete Appl. Math., 2001, 111(1,2), 189–197.
Solov'eva F. I., Avgustinovich S. V., Lobstein A. Intersection, matrices for partitions by binary perfect codes // IEEE Trans. Inform. Theory, 2001, 47(4), 1621–1624.
