The size of a (v,5,2,1) optical orthogonal code (OOC) is shown to be at most equal to ⌈v/12⌉ when v ≡ 11 (mod 132) or v ≡ 154 (mod 924), and at most equal to ⌊v/12⌋ in all the other cases. Thus a (v,5,2,1)-OOC is naturally said to be optimal when its size reaches the above bound. Many direct and recursive constructions for infinite classes of optimal (v,5,2,1)-OOCs are presented giving, in particular, a very strong indication about the existence of an optimal (p,5,2,1)-OOC for every prime p ≡ 1 (mod 12).
On optimal (v,5,2,1) optical orthogonal codes
BURATTI, Marco;
2013
Abstract
The size of a (v,5,2,1) optical orthogonal code (OOC) is shown to be at most equal to ⌈v/12⌉ when v ≡ 11 (mod 132) or v ≡ 154 (mod 924), and at most equal to ⌊v/12⌋ in all the other cases. Thus a (v,5,2,1)-OOC is naturally said to be optimal when its size reaches the above bound. Many direct and recursive constructions for infinite classes of optimal (v,5,2,1)-OOCs are presented giving, in particular, a very strong indication about the existence of an optimal (p,5,2,1)-OOC for every prime p ≡ 1 (mod 12).File in questo prodotto:
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