Abstract
Optimal (9p,4,1) optical orthogonal codes (OOCs) are constructed for all primes p congruent to 1 modulo 4. Direct constructions with explicit codewords are presented for the case $p \equiv 13 \mbox{mod} 24$, and Weil's theorem on character sums is used to settle the cases $p \equiv 1,5,17 \mbox{mod} 24$. By applying a known recursive construction, optimal (9v,4,1)-OOCs are obtained for all v, a product of primes congruent to 1 modulo 4.
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