Some progress on (v, 4, 1) difference families and optical orthogonal codes

@article{Abel2004SomePO,
  title={Some progress on (v, 4, 1) difference families and optical orthogonal codes},
  author={R. Julian R. Abel and Marco Buratti},
  journal={J. Comb. Theory, Ser. A},
  year={2004},
  volume={106},
  pages={59-75}
}
Some new classes of optimal (v, 4, 1) optical orthogonal codes are constructed. First, mainly by using perfect difference families, we establish that such an optimal OOC exists for v ≤ 408, v ≠ 25. We then look at larger (p, 4, 1) OOCs with p prime; some of these codes have the nice property that the missing differences are the (r - 1)th roots of unity in Zp, (r being the remainder of the Euclidean division of p by 12) and we prove that for r = 5 or 7 they give rise to (rp, 4,1) difference… CONTINUE READING

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