Galina T. Bogdanova

Bounds and constructions for ternary constant-composition codes

The problem of determining the maximum size of a ternary code is considered, under the restriction that each symbol should appear a given number of times in each codeword. Upper and lower bounds on the size of such codes under the Hamming metric are discussed, where the lower bounds follow from constructions of good codes. Some of the results are obtained by explicitly finding codes by computer search. A table of exact values and best known bounds on the maximum size for codes of length at most 10 is presented.

Error-correcting codes over an alphabet of four elements

The problem of finding the values of Aq(n,d)—the maximum size of a code of length n and minimum distance d over an alphabet of q elements—is considered. Upper and lower bounds on A4(n,d) are presented and some values of this function are settled. A table of best known bounds on A4(n,d) is given for n ≤ 12. When q ≤ M < 2q, all parameters for which Aq(n,d) = M are determined.

On the construction of q-ary equidistant codes

The problem of constructing equidistant codes over an alphabet of an arbitrary size q is considered. Some combinatorial constructions and computer-based search methods are presented. All maximal equidistant codes with distances 3 and 4 are found.

Enumeration of Optimal Ternary Constant-Composition Codes

The problem of classification of optimal ternary constant-composition codes is considered. Using a combinatorial-computer method, the number of inequivalent codes is determined for 3 ≤ d ≤ n ≤ 10.

Bounds on codes over an alphabet of five elements

Abstract We consider the problem of finding bounds and exact values of A 5 (n,d) — the maximum size of a code of length n and minimum distance d over an alphabet of 5 elements. Using a wide variety of constructions and methods, a table of bounds on A 5 (n,d) for n⩽11 is obtained.

NEW TERNARY AND QUATERNARY CONSTANT-WEIGHT EQUIDISTANT CODES

In this paper we consider the problem of finding bounds on the size of ternary and quaternary constant-weight equidistant codes with 2 ≤ w < n ≤ 10. Optimal ternary and quaternary constant-weight equidistant codes have been constructed by combinatorial and computer methods. All open cases for the size of optimal ternary and quaternary constant-weight equidistant codes have been closed.

Use of dynamic technologies for web-enabled database management systems

In this paper we consider some computer systems and the dynamic Web technologies they are using, Specific applications are developed, clinic and studying systems, and their programming models are described, These models apply some dynamic Web technologies for creation of database management systems.

Software Approaches and Methods to Ensure the Security of Interactive Systems

Abstract In the paper are studied methods for protection of interactive systems and digital archives against unauthorized distribution of digital content. We make an overview of steganographic methods and image protection schemes. An improved watermark error correction scheme is presented. The studies contribute to the overall development of the North+region, provide future generations with widespread public access to digital materials. We achieve a long-term storage, secure data protection and interactive web presence.

QPlus: computer package for coding theory research and education

A shared computer tool QPlus for studying coding theory studying is presented. The system offers computations over Z q ={0, 1, …, q−1} (q<256) and includes modular arithmetic, elementary number theory, vectors and matrices arithmetic and an environment for research on q-ary codes – linear, constant-weight and equidistant codes. QPlus includes a DLL library package that implements coding theory algorithms. We explore the problem of finding bounds on the size of q-ary codes by computer methods. Some examples for optimal equidistant codes and constant-weight equidistant codes that have been constructed by computer methods developed in QPlus are described. We also research some optimal linear codes.

Digitalization and security of "Bulgarian Folklore Heritage" archive

We investigate methods and techniques used in digitalization and security of the objects in multimedia folklore archive. This archive consists of unique folklore artifacts stored and annotated in the National center for non-material cultural heritage, Institute of Folklore, Bulgarian Academy of Sciences. First we investigate techniques for digitalization of different multimedia types -- text, images, audio and video. We apply this research to selected collections of artifacts. Next we determine metadata appropriate to investigated objects. Third we describe several methods applied for securing the intellectual property and author rights. This includes digital watermarking and error-correcting codes. Finally we describe process of creation and organization of digital folklore archive that consists of digitalized objects with added metadata and security data.