Тодоров,
Тодор
(2011)
QPlus  computer package for coding theory research and education
International Journal of Computer Mathematics, vol. 88, No. 3, 2011, pp. 443451, ISSN: 00207160
A shared computer tools QPlus for coding theory studying is presented. The system offers computations over Zq = {0, 1,. .. , q − 1} (q < 256) and includes modular arithmetic, elementary number theory, vectors and matrices arithmetic and an environment for research on qary codes – linear, constantweight and equidistant codes. Optimal ternary constantweight codes, binary and ternary equidistant codes have been constructed by our computer methods. QPlus includes a DLL library package that implements coding theory algorithms. 1. Introduction. The main subject of the research in this work are the optimal qary codes. We consider several classes of codes – linear codes, constantweight codes, constantcomposition codes and equidistant codes. Let us introduce some basic notations which we need to describe the results. Let Q be an alphabet of q ≥ 2 elements. We consider the set Q n , consisting of ordered ntuples of elements of Q. The Hamming distance between two ntuples of Q n is defined as the number of coordinates, in which they differ. We call any subset of Q n a qary code of length n or simply a code over the alphabet Q. The elements of a code are called codewords. An important parameter of each code is its minimum distance – the smallest possible Hamming distance between two different codewords. An (n, M, d) qcode is a qary code of length n containing M codewords, and of minimum distance d. The alphabet Q can consist of the elements of the set Z q = {0, 1,. .. , q − 1}. If q is a prime power and the alphabet Q = GF (q) is a finite field of q elements then GF n (q) is an ndimensional vector space. In this paper a set of computer tools for coding theory research is presented. The system offers computations over Z q = {0, 1,. .. , q − 1}, q < 256 (modular arithmetic, elementary number theory, calculations with vectors, matrices), environments for research on qary codes (linear, constantweight, equidistant) and a DLL library (Delphi's components). By the help of QPlus optimal ternary constantweight codes, binary and ternary equidistant codes have been constructed.
Статия
Природни науки, математика и информатика
Природни науки, математика и информатика
Информатика и компютърни науки
Natural sciences, mathematics and informatics
Natural sciences, mathematics and informatics
Informatics and Computer Science
Издадено
16643
Тодор Тодоров
