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Download Algebraic Aspects of Digital Communications: Volume 24 NATO by T. Shaska, E. Hasimaj PDF

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By T. Shaska, E. Hasimaj

Advancements of the previous few a long time in electronic communications have created an in depth hyperlink among arithmetic and components of machine technology and electric engineering. A collaboration among such components now turns out very usual, because of difficulties which require deep wisdom and services in every one zone. Algebra and a few of its branches, corresponding to algebraic geometry, computational algebra, team conception, etc., have performed a unique function in such collaboration. for that reason, there at the moment are disciplines akin to coding concept and cryptography, that are thought of a mixture of arithmetic, desktop technology and electric engineering. Algebraic features of electronic Communications makes a speciality of connections among algebra, algebraic geometry, quantity idea, graph idea and comparable parts of arithmetic with coding conception and cryptography. This booklet is geared toward mathematicians, computing device scientists and engineers who have to discover ties among algebra and coding idea and cryptography. IOS Press is a global technological know-how, technical and scientific writer of top quality books for teachers, scientists, and execs in all fields. the various components we put up in: -Biomedicine -Oncology -Artificial intelligence -Databases and knowledge platforms -Maritime engineering -Nanotechnology -Geoengineering -All features of physics -E-governance -E-commerce -The wisdom economic climate -Urban reports -Arms keep watch over -Understanding and responding to terrorism -Medical informatics -Computer Sciences

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Read Online or Download Algebraic Aspects of Digital Communications: Volume 24 NATO Science for Peace and Security Series - D: Information and Communication Security (Nato Science ... D: Information and Communication Security) PDF

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Extra info for Algebraic Aspects of Digital Communications: Volume 24 NATO Science for Peace and Security Series - D: Information and Communication Security (Nato Science ... D: Information and Communication Security)

Example text

A Reed-Solomon (RS) code has generator of the form k−1 g(x) = i=1 (x − αi ), where α is a primitive root of 1 in Fq . Aside: All affine codes of dimension r and word length q r−1 are isometric (namely, the codewords of one can be obtained from those of the other by a fixed permutation of the entries xi → xσ(i) and multiplication of each entry by a non-zero λi ∈ Fq ) and are called Reed-Muller codes. To make Goppa’s definition appear more natural we give Reed and Solomon’s original approach. Let P1 = α0 , .

Theory, IT-47 (2001), 1575–1580. [25] F. J. MacWilliams, A. M. Odlyzko, N. J. A. Sloane, and H. N. Ward, Self-dual codes over GF(4), J. Comb. Theory, 25A (1978), 288–318. [26] E. M. Rains and N. J. A. Sloane, Self-dual codes, in “Handbook of Coding Theory,” eds. V. S. Pless and W. C. Huffman. Amsterdam: Elsevier, 1998, pp. 177–294. [27] R. P. , 8 (2002), 34–51. [28] Z. Varbanov, Some new results for additive self-dual codes over GF(4), Serdica J. Computing, 1 (2007), 213–227. [29] V. Y. Yorgov, Binary self-dual codes with automorphisms of odd order, Problems Inform.

A. Sloane, Self-dual codes and invariant theory. Springer-Verlag (2006). [11] G. Nebe, Kneser-Hecke-operators in coding theory. Abh. Math. Sem. Univ. Hamburg 76 (2006) 79-90 [12] G. Nebe, Finite Weil-representations and associated Hecke-algebras. (preprint) [13] E. M. Rains and N. J. A. Sloane, Self-dual codes, in Handbook of Coding Theory, ed. V. S. Pless and W. C. Huffman, Elsevier, Amsterdam, 1998, pp. 177–294. [14] E. Rains, Shadow bounds for self-dual codes. IEEE Trans. Inform. Theory 44 (1998), no.

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