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The Discovery of Simple 7Designs with Automorphism Group ...
, 1995
"... 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 graphical interface modules. Standard applications can be run automatically whereas research projects mostly ..."
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Cited by 10 (7 self)
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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 graphical interface modules. Standard applications can be run automatically whereas research projects mostly require small C or C++ programs. The basic philosophy behind the system is to transform problems into standard problems of e.g. group theory, graph theory, linear algebra, graphics, or databases and then to use highly specialized routines from that field to tackle the problems. The transformations required often follow the same principles especially in the case of generation and isomorphism testing.
Isometry Classes of Indecomposable Linear Codes
 Proc. Int. Symp., AAECC11, Paris 1995, volume 948 of Lecture
, 1995
"... In the constructive theory of linear codes, we can restrict attention to the isometry classes of indecomposable codes, as it was shown by Slepian. ..."
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Cited by 9 (2 self)
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In the constructive theory of linear codes, we can restrict attention to the isometry classes of indecomposable codes, as it was shown by Slepian.
Enumeration of linear codes by applying methods from algebraic combinatorics
 Grazer Math. Ber
, 1996
"... It is demonstrated how classes of linear (n, k)codes can be enumerated using cycle index polynomials and other methods from algebraic combinatorics. Some results of joined work [9] with Prof. Kerber from the University of Bayreuth on the enumeration of linear codes over GF (q) are presented. Furthe ..."
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Cited by 5 (0 self)
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It is demonstrated how classes of linear (n, k)codes can be enumerated using cycle index polynomials and other methods from algebraic combinatorics. Some results of joined work [9] with Prof. Kerber from the University of Bayreuth on the enumeration of linear codes over GF (q) are presented. Furthermore I will give an introduction to enumeration under finite group actions. At first let me draw your attention to the enumeration of linear codes. Let p be a prime and let q be a power of p then GF (q) denotes the finite field of q elements. A linear (n, k)code over the Galois field GF (q) is a kdimensional subspace of the vector space GF (q) n. As usual codewords will be written as rows x = (x1,..., xn). A k × nmatrix Γ over GF (q) is called a generator matrix of the linear (n, k)code C, if and only if the rows of Γ form a basis of C, so that C = {x · Γ  x ∈ GF (q) k}. The Hamming distance d(x, y): = {i ∈ n⎪xi � = yi}  is a metric on GF (q) n. (The set of integers from 1 to n will be indicated as n.) The minimal distance d(C) of a code C is given by d(C): = min
Construction of Combinatorial Objects
, 1995
"... Isomorphism problems often can be solved by determining orbits of a group acting on the set of all objects to be classified. The paper centers around algorithms for this topic and shows how to base them on the same idea, the homomorphism principle. Especially it is shown that forming Sims chains, u ..."
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Cited by 1 (1 self)
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Isomorphism problems often can be solved by determining orbits of a group acting on the set of all objects to be classified. The paper centers around algorithms for this topic and shows how to base them on the same idea, the homomorphism principle. Especially it is shown that forming Sims chains, using an algorithmic version of Burnside's table of marks, computing double coset representatives, and computing Sylow subgroups of automorphism groups can be explained in this way. The exposition is based on graph theoretic concepts to give an easy explanation of data structures for group actions.