Универсални граници за мощността и енергията на кодове в Хемингови пространства
Ключови думи :
пространства на Хеминг, граници на Левенщейн, потенциални функции, енергия на код, кодове коригиращи грешки, τ -дизайни, променливи по знак меркиАбстракт
В статията се представят систематизирано резултати за универсалните граници за размерността и енергията на кодовете в Хемингови пространства. Универсалността означава, че границите са валидни за голям клас от потенциални функции (най-важните от тях са в сила за абсолютно монотонни потенциали). Освен това, като се използват променливи по знак мерки, положително определени до дадена степен, са получени горни граници от тип Левенщейн за мощността на кодовете с дадено минимално и максимално разстояние и универсални долни граници на потенциалната енергия за кодове с дадено максимално разстояние и мощност. Представените методи и техники могат да се разглеждат като обобщение и продължение на разработената от Левенщейн теория.
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