Codes, Curves, and Signals: Common Threads in Communications - download pdf or read online

By Tom Høholdt (auth.), Alexander Vardy (eds.)

ISBN-10: 1461373301

ISBN-13: 9781461373308

ISBN-10: 1461551218

ISBN-13: 9781461551218

Codes, Curves, and indications: universal Threads in Communications is a set of seventeen contributions from best researchers in communications. The publication offers a consultant cross-section of leading edge modern study within the fields of algebraic curves and the linked interpreting algorithms, using sign processing ideas in coding idea, and the appliance of information-theoretic tools in communications and sign processing. The ebook is geared up into 3 components: Curves and Codes, Codes and signs, and indications and Information.
Codes, Curves, and indications: universal Threads in Communications is a tribute to the large and profound impression of Richard E. Blahut at the fields of algebraic coding, details thought, and electronic sign processing. the entire individuals have separately and jointly devoted their paintings to R. E. Blahut.
Codes, Curves, and indications: universal Threads in Communications is a superb reference for researchers and professionals.

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Additional resources for Codes, Curves, and Signals: Common Threads in Communications

Sample text

VAN DER GEER AND M. VAN DER VLUGT, Quadratic forms, generalized Hamming weights of codes, and curves with many rational points, J. Number Theory, vol. 59, pp. 20-36, 1996. [12) ___ , Generalized Hamming weights of codes and curves over finite fields with many rational points, in Israel Math. , vol. 417-432, 1996. P. HANSEN, Codes from the Klein quartic, ideals, and decoding, IEEE 'frans. Inform. Theory, vol. 923-925, 1987. [14) T. H. VAN LINT, AND R. S. C. Huffman (Editors), Amsterdam: Elsevier, 1998.

We have 011·· ·15 = 201·· ·15+121·· ·15. Using Lemma3, the second term is consistent with 110·· ·15. 15) < w(201 .. 15), we have 011· . ·15 '" 210· . ·15 and the lemma is true for k + 1. • Lemma 5. .. 011· .. 12 ... '" ... 201 ... 12 .... Proof. Repeatedly using 20 we have: ... 201 ... 12 . = 01 + 12 and in the last step using 22 = 11 +00, = ... 011 ... 12 ... + ... 121 ... 12 .. = ···011··· 12 ... + ... 110 ... 12 ... + ... 102 ... 12 ... = = = ···011··· 12 ... + ... 110 ... 12· .. + ... + ...

11 .. + .. ·101·· ·00··· Among the right side terms, .. ·110·· ·12··· has the maximal weight and its weight is equal to the weight of ... 201 ... 12 .. '. The proof is thus complete. • Using Lemmas 3, 4, and 5, we have the following good terms for hr. Theorem 6. Let am, ... , ap E {O, 1}. Then: am' .. apOO .. ·011 ... 12aq ••• a25 '" am ... apOO .. ·201 ... 12aq ••• a25 am ... ap002 ... 101 ... 12aq ••• a25 am ... ap021· .. 101· .. 12aq ••• a25 am'" ap21 .. ·101·· . 12aq ••• a25 As an application of Theorem 6, we have for example: 0011000115", 0011002015 '" 0011021015 '" 0011211015 '" 0201211015 '" 2101211015.

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Codes, Curves, and Signals: Common Threads in Communications by Tom Høholdt (auth.), Alexander Vardy (eds.)


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