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- Title
Maximal (v , k , 2, 1) Optical Orthogonal Codes with k = 6 and 7 and Small Lengths.
- Authors
Baicheva, Tsonka; Topalova, Svetlana
- Abstract
Optical orthogonal codes (OOCs) are used in optical code division multiple access systems to allow a large number of users to communicate simultaneously with a low error probability. The number of simultaneous users is at most as big as the number of codewords of such a code. We consider (v , k , 2 , 1) -OOCs, namely OOCs with length v, weight k, auto-correlation 2, and cross-correlation 1. An upper bound B 0 (v , k , 2 , 1) on the maximal number of codewords of such an OOC was derived in 1995. The number of codes that meet this bound, however, is very small. For k ≤ 5 , the (v , k , 2 , 1) -OOCs have already been thoroughly studied by many authors, and new upper bounds were derived for (v , 4 , 2 , 1) in 2011, and for (v , 5 , 2 , 1) in 2012. In the present paper, we determine constructively the maximal size of (v , 6 , 2 , 1) - and (v , 7 , 2 , 1) -OOCs for v ≤ 165 and v ≤ 153 , respectively. Using the types of the possible codewords, we calculate an upper bound B 1 (v , k , 2 , 1) ≤ B 0 (v , k , 2 , 1) on the code size of (v , 6 , 2 , 1) - and (v , 7 , 2 , 1) -OOCs for each length v ≤ 720 and v ≤ 340 , respectively.
- Subjects
ORTHOGONAL codes; CODE division multiple access; HADAMARD codes; ERROR probability
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 11, p2457
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11112457