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Constant weight codes with package CodingTheory.m in Mathematica. (English) Zbl 1102.68737

Bubak, Marian (ed.) et al., Computational science – ICCS 2004. 4th international conference, Kraków, Poland, June 6–9, 2004. Proceedings, Part IV. Berlin: Springer (ISBN 3-540-22129-8/pbk). Lecture Notes in Computer Science 3039, 370-375 (2004).
Summary: The author offers a further development of the package CodingTheory.m [the author, Lect. Notes Comput. Sci. 2657, 737–746 (2003; Zbl 1033.94566)] in the direction of research of properties and parameters of constant weight codes (lower and upper bounds) and also using the Table of Constant Weight Binary Codes [online version, N. J. A. Sloane: Home Page http://www.research.att.com/\(\sim\)njas/codes/Andw/] and the table of upper bounds on \(A(n, d, w)\) (which in many cases also gives lower bounds) maintained by E. Agrell, A. Vardy and K. Zeger, which is an electronic supplement to their paper “Upper bounds for constant-weight codes” [IEEE Trans. Inf. Theory 46, No. 7, 2373–2395 (2000; Zbl 0997.94036), http://www.s2.chalmers.se/\(\sim\)agrell/bounds/cw.html]. The offered package allows one 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 some construction of codes as union of two codes with parameters \((n, 2 a, a+ b)\) and \((m, 2 b, a + b)\), that in some cases gives codes that are better than codes obtained with using Juxtaposing.
For the entire collection see [Zbl 1051.68007].

MSC:

68W30 Symbolic computation and algebraic computation
94B05 Linear codes (general theory)
94B60 Other types of codes
94B65 Bounds on codes
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