Constant weight codes with package CodingTheory.m in mathematica

Abstract

The author offers the further development of package CodingTheory.m [1] in the direction of research of properties and parameters of Constant weight codes (lower and upper bounds) based on works [2], [3] and also using the Table of Constant Weight Binary Codes (online version, Neil J. A. Sloane: Home Page http://www.research.att.com/∼njas/codes/Andw/) and the table of upper bounds on A(n, d, w) (which in many cases also gives lower bounds) maintained by Erik Agrell, Alexander Vardy and Kenneth Zeger, and which is an electronic supplement to their paper Upper bounds for constant-weight codes, http://www.s2.chalmers.se/∼agrell/bounds/cw.html. The offered package allows to carry out the comparative analysis of parameters of new codes with classical upper bounds such as Johnson bound, Linear programming (Ph Delsarte) bound ..., and also with already available classes of codes. As an example we consider a some construction of codes as union of two codes with parameters (n, 2a, a+b) and (m, 2b, a + b), that in some cases gives codes the best than codes obtained with use Juxtaposing. © Springer-Verlag Berlin Heidelberg 2004.