## QPlus - computer package for coding theory research and education

 Тодоров, Тодор (2011) QPlus - computer package for coding theory research and education International Journal of Computer Mathematics, vol. 88, No. 3, 2011, pp. 443-451, ISSN: 0020-7160 Резюме / Abstract  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 q-ary codes – linear, constant-weight and equidistant codes. Optimal ternary constant-weight 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 q-ary codes. We consider several classes of codes – linear codes, constant-weight codes, constant-composition 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 n-tuples of elements of Q. The Hamming distance between two n-tuples of Q n is defined as the number of coordinates, in which they differ. We call any subset of Q n a q-ary 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) q-code is a q-ary 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 n-dimensional 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 q-ary codes (linear, constant-weight, equidistant) and a DLL library (Delphi's components). By the help of QPlus optimal ternary constant-weight codes, binary and ternary equidistant codes have been constructed. Вид:   Статия Ключови думи:   Области: Природни науки, математика и информатика Природни науки, математика и информатика Информатика и компютърни науки Subjects: Natural sciences, mathematics and informatics Natural sciences, mathematics and informatics Informatics and Computer Science Статус:  Издадено Идентификационен номер:   16643 Автор:  Тодор Тодоров

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