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Optimal (v, 4, 2, 1) optical orthogonal codes (OOC) with v <= 75 and v = 71 are classified up to equivalence. One (v, 4, 2, 1) OOC is presented for all v ≤ 181, for which an optimal OOC exists.
A spread is a set of lines of P G(d, q), which partition the point set. A parallelism is a partition of the set of lines by spreads. There is a one-to-one correspondence between the parallelisms of P G(3, 4) and the resolutions of the 2-(85,5,1) design of its points and lines. We construct 482 non isomorphic parallelisms with automorphisms of order 7.
A parallelism in $$PG(n,q)$$ P G ( n , q ) is transitive if it has an automorphism group which is transitive on the spreads. A parallelism is regular if all its spreads are regular. In $$PG(3,4)$$ P G ( 3 , 4 ) no examples of transitive and no regular parallelisms are known. Transitive parallelisms in $$PG(3,4)$$ P G ( 3 , 4 ) must have automorphisms of… (More)