Download Applied Algebra, Algebraic Algorithms and Error-Correcting by James L. Massey (auth.), Serdar Boztaş, Igor E. Shparlinski PDF

By James L. Massey (auth.), Serdar Boztaş, Igor E. Shparlinski (eds.)

ISBN-10: 3540429115

ISBN-13: 9783540429111

The AAECC Symposia sequence was once all started in 1983 through Alain Poli (Toulouse), who, including R. Desq, D. Lazard, and P. Camion, equipped the ?rst convention. initially the acronym AAECC intended “Applied Algebra and Error-Correcting Codes”. through the years its which means has shifted to “Applied Algebra, Algebraic Algorithms, and Error-Correcting Codes”, re?ecting the turning out to be value of complexity in either deciphering algorithms and computational algebra. AAECC goals to inspire cross-fertilization among algebraic equipment and their purposes in computing and communications. The algebraic orientation is in the direction of ?nite ?elds, complexity, polynomials, and graphs. The functions orientation is in the direction of either theoretical and useful error-correction coding, and, in view that AAECC thirteen (Hawaii, 1999), in the direction of cryptography. AAECC was once the ?rst symposium with papers connecting Gr¨obner bases with E-C codes. The stability among theoretical and functional is meant to shift frequently; at AAECC-14 the focal point was once at the theoretical aspect. the most topics coated have been: – Codes: iterative interpreting, deciphering tools, block codes, code building. – Codes and algebra: algebraic curves, Gr¨obner bases, and AG codes. – Algebra: jewelry and ?elds, polynomials. – Codes and combinatorics: graphs and matrices, designs, mathematics. – Cryptography. – Computational algebra: algebraic algorithms. – Sequences for communications.

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Hence, the first assertion of the lemma follows. The second assertion follows from the first. 1 U(M ) and SU(M ) denote the group of unitary M × M -matrices and the groups of unitary M × M -matrices of determinant one, respectively. Design of Differential Space-Time Codes Using Group Theory 27 The lemma shows that A(2, L) ≥ B(2, L) where B(2, L) is half the minimum distance of the best spherical code with L points on S3 . This number has been studied quite extensively, and very good upper and lower bounds are known for it [6].

Handbook of Coding Theory. V. C. , Amsterdam, 1998. 24. : The [18,9,6] code is unique. Discrete Math. 106/107 (1992) 439–448. 25. : A bound for divisible codes. IEEE Trans. Inform. Th. 38 (1992) 191– 194. com Abstract. It is well-known that multiple transmit and receiving antennas can significantly improve the performance of wireless networks. , mobile communication) leads to an interesting packing problem for unitary matrices. Surprisingly, the latter problem is related to certain aspects of finite (and infinite) group theory.

To appear. com. 17. J. Stilwell. The story of the 120-cell. Notices of the AMS, 48:17–24, 2001. 18. V. Tarokh, N. Seshadri, and A. R. Calderbank. Space-time codes for high data rate wireless communication: Performance criterion and code construction. IEEE Trans. Info. Theory, 44:744–765, 1998. 19. I. E. Telatar. Capacity of multi-antenna gaussian channels. Technical report, Bell Laboratories, Lucent Technologies, 1995. ¨ 20. H. Zassenhaus. Uber endliche Fastk¨orper. Abh. Math. Sem. Hamburg, 11:187–220, 1936.

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