Description: Codes and Curves (Student Mathematical Library, Vol. 7)by Judy L. WalkerAmerican Mathematical Society (2000)When information is transmitted, errors are likely to occur. This problem has become increasingly important as tremendous amounts of information are transferred electronically every day. Coding theory examines efficient ways of packaging data so that these errors can be detected, or even corrected.The traditional tools of coding theory have come from combinatorics and group theory. Since the work of Goppa in the late 1970s, however, coding theorists have added techniques from algebraic geometry to their toolboxes. In particular, by re-interpreting the Reed-Solomon codes as coming from evaluating functions associated to divisors on the projective line, one can see how to define new codes based on other divisors or on other algebraic curves. For instance, using modular curves over finite fields, Tsfasman, Vladut, and Zink showed that one can define a sequence of codes with asymptotically better parameters than any previously known codes. This book is based on a series of lectures the author gave as part of the IAS/Park City Mathematics Institute (Utah) program on arithmetic algebraic geometry. Here, the reader is introduced to the exciting field of algebraic geometric coding theory. Presenting the material in the same conversational tone of the lectures, the author covers linear codes, including cyclic codes, and both bounds and asymptotic bounds on the parameters of codes. Algebraic geometry is introduced, with particular attention given to projective curves, rational functions and divisors. The construction of algebraic geometric codes is given, and the Tsfasman-Vladut-Zink result mentioned above is discussed. NOAZ-2023-0712-01 Please visit my store for other interesting and unique items! Would you like to purchase multiple items at the same time? Please ask about combined shipping! Welcome! I'm Mary aka Maryesterday, a gal who has lived as a vintage "time traveler" for over 20 years. The past? I'm there! In order to fuel my passion for all things vintage, forgotten, antique, mysterious, and mid-century modern, I've turned this into my full time business -- I support myself by sharing great finds and lost treasures I unearth in my real-life retro adventures. I'm here on eBay to share them with you. I try to set the BIN price fairly for a fast sale. If you are truly interested in this item but have reservations about the price, please do not hesitate to make what you feel is a fair offer. All proceeds of this listing go to help an independent outsider artist working in the field of literature and creative writing. Visit my store for collectibles, lost ephemera, cool clothing, vintage obscure and rare records and recordings (a great way to "time travel"!), and interesting retro reads. I have a lot of books, because there's no better way to time travel than in the pages of a good old book. Try it once, and you'll be hooked for life! I hope you enjoy the time you spend with me here -- and have a nice yesterday!
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End Time: 2025-01-13T01:46:29.000Z
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