By Giovanni Di Crescenzo (auth.), Jacques Calmet, Willi Geiselmann, Jörn Müller-Quade (eds.)

ISBN-10: 3540899936

ISBN-13: 9783540899938

This Festschrift quantity includes the court cases of the convention Mathematical equipment in desktop technological know-how, MMICS 2008, which was once held in the course of December 17-19, 2008, in Karlsruhe, Germany, in reminiscence of Thomas Beth.

The topics of the convention mirrored the numerous pursuits of Thomas Beth. even if, those pursuits might sound various, mathematical tools and particularly algebra as a language constituted the typical denominator of all of his clinical achievements.

The 12 contributed talks offered have been rigorously chosen from 30 submissions and canopy the subjects cryptography, designs, quantum computing, algorithms, and coding idea. additionally, this quantity comprises invited talks held on the convention. One specializes in the realm of coding concept and symbolic computation, a space specially liked by way of Thomas Beth, since it combines algebra and algorithmics. the opposite one discusses quantum info, which back was once a spotlight of Thomas Beth’s learn.

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**Extra resources for Mathematical Methods in Computer Science: Essays in Memory of Thomas Beth**

**Sample text**

Des. Codes Cryptography 34(1), 55–70 (2005) 42 A. Kohnert and S. Kurz 8. : Construction of (n, r)-arcs in P G(2, q). Innov. Incidence Geom. 1, 133–141 (2005) 9. : On the orbits of Singer groups and their subgroups. Electronic Journal Comb. 9(1), 10 p. (2002) 10. 3528) 11. : Error-Correcting codes in projective space. In: ISIT Proceedings, 5 p. (2008) 12. 2262) 13. : Coding for errors and erasures in random network coding. IEEE Transactions on Information Theory 54(8), 3579–3391 (2008) 14. : t-designs on hypergraphs.

In the third row of each entry we give the size lb of a constant dimension6 code and the best found upper bound ub in the format lb − ub. As described in Section 3 for a given group our problem corresponds to several versions of feasibility or optimization problems. To obtain the lower bounds we have used the LLL based algorithm, the coding theoretic motivated heuristic and the ILOG CPLEX solver for integer linear programs. The upper bounds were obtained by the CPLEX solver stopping the solution process after a reasonable time.

I in the ﬁnal state C |ψ0 : p0 − p1 = ψ0 | C † Z1 C |ψ0 (2) This computation suﬃces to simulate the output (as also p0 + p1 = 1). Now Z1 is clearly a product of Pauli operations so C † Z1 C also has the product form P1 ⊗ . . ⊗ Pn for Pauli operations Pi (whose identity can be determined in linear time by an update rule for successive conjugations by the elementary gates in the circuit). Hence if |ψ0 = |a1 . . |an is any product state we get n p0 − p1 = ak | Pk |ak (3) k=1 which can clearly be calculated in time O(n) (as a product of n terms of ﬁxed size) giving an eﬃcient (linear time) simulation of the Cliﬀord circuit.

### Mathematical Methods in Computer Science: Essays in Memory of Thomas Beth by Giovanni Di Crescenzo (auth.), Jacques Calmet, Willi Geiselmann, Jörn Müller-Quade (eds.)

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