Нови оптимални (v, k, 1) оптични ортогонални кодове с k = 3, 5, 6
DOI :
https://doi.org/10.55630/mem.2026.55.329-339Ключови думи :
теория на кодирането, оптимален оптичен ортогонален код, двоичен константно тегловен циклично пермутационен код, циклични разностни фамилии, цикличен дизайнАбстракт
Известните класификации на оптимални оптични ортогонални кодове с малки k показват, че когато дължината на кода v нараства, броят на нееквивалентните кодове се увеличава много бързо. Това или прави пълната класификация за относително големи стойности на v невъзможна, или броят на получените кодове е толкова голям, че е много трудно да се избере сред тях код с необходимите свойства. Ето защо в настоящата работа не получаваме всички кодове с разглежданите параметри. Конструираме множества от нови оптимални (v, k, 1) оптични ортогонални кодове с k = 3, 5 и 6 за относително малки стойности на дължините на кода v, за които не са известни резултати от класификацията. Кодовете във всеки от тези множества се различават един от друг по много кодови думи. Те могат да бъдат използвани в практически приложения, както и в по-нататъшни изследвания по темата.
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