Gennadiy Khalimov

Krivye Gurvitsa: Postroenie I Primenenie Dlya Universal'nogo Kheshirovaniya Gennadiy Khalimov Russian edition

Lineynye vektornye prostranstva assotsiirovannye s funktsional'nym polem algebraicheskikh krivykh opredelyayut konstruktsii algebrogeometricheskikh kodov i kodovye konstruktsii universal'nogo kheshirovaniya. Problematika postroeniya kodovykh skhem na osnove algebrogeometricheskogo predstavleniya zaklyuchaetsya v vybore algebraicheskikh krivykh s trebuemymi parametrami, prezhde vsego s kak mozhno bol'shim otnosheniem chisla tochek krivoy k eye rodu, a takzhe s aspektami realizatsii vychisleniy v konechnom pole, prezhde vsego prostotoy vychisleniy i soglasovannost'yu s predstavleniem informatsionnykh dannykh. Krivye Gurvitsa yavlyayutsya klassicheskimi ploskimi krivymi. Mnogoobrazie krivykh opredelyaetsya pokazatelyami stepeney ot dvukh peremennykh i yavlyaetsya sushchestvenno, bol'shim po sravneniyu s krivymi Ferma. Predstavleny rezul'taty usloviy sushchestvovaniya i otsenki parametrov obobshchennykh krivykh Gurvitsa, maksimal'nykh krivykh, krivykh s bol'shim chislom tochek v rasshirennykh konechnykh polyakh i prostom pole. Privodyatsya algoritmy postroenie krivykh Gurvitsa zadannogo roda bez ogranicheniy na pokazateli stepeni nad proizvol'nym konechnym polem i primeneniya dlya universal'nogo kheshirovaniya.