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In this correspondence, we compute the weight enumerators of various quadratic residue codes over F/sub 2/ and F/sub 3/, together with certain codes of related families like the duadic and the quadratic double circulant codes. We use a parallel algorithm to find the number of codewords of a given (not too high) weight, from which we deduce by usual… (More)
New linear codes (sometimes optimal) over the finite field with q elements are constructed. In order to do this, an equivalence between the existence of a linear code with a prescribed minimum distance and the existence of a solution of a certain system of Diophantine linear equations is used. To reduce the size of the system of equations, the search for… (More)
Kramer-Mesner matrices have been used as a powerful tool to construct t-designs. In this paper we construct Kramer-Mesner matrices for xed values of k and t in which the entries are polynomials in n the number of vertices of the underlying graph. From this we obtain an elementary proof that with a few exceptions S 2] n is a maximal subgroup of S (n 2) or A… (More)
This correspondence revisits the idea of constructing a binary [mn,mk] code from an [n,k] code over F/sub 2//sup m/ by concatenating the code with a suitable basis representation of F/sub 2//sup m/ over F/sub 2/. We construct two nonequivalent examples of doubly even self-dual binary codes of length 160 which turn out to be of minimum distance 24. This… (More)
Lattice basis reduction in combination with an eecient backtracking algorithm is used to nd all (4 996 426) simple 7-(33,8,10) designs with automor-phism group P?L(2,32).
A computer package is being developed at Bayreuth for the generation and investigation of discrete structures. The package is a C and C++ class library of powerful algorithms endowed with some graph-ical interface modules. Some standard applications can be run automatically whereas research projects mostly require small C or C++ programs. The basic… (More)
We describe a computer search for simple designs with prescribed automor-phism groups yielding designs with parameter sets 7-In several of these cases we are able to determine the exact number of isomorphism types of designs with that prescribed automorphism group. c