Bounds and constructions of optimal (n, 4, 2, 1) optical orthogonal codes

  • Authors:

  • Koji Momihara;Marco Buratti

  • Affiliations:

  • Graduate School of Information Science, Nagoya University, Nagoya, Japan;Dipartimento di Matematica e Informatica, Università di Perugia, Perugia, Italy

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2009

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Abstract

In this paper, a tight upper bound on the maximum possible code size of (n 4, 2, 1,)-OOCs and some direct and recursive constructions of optimal (n 4, 2, 1,)-OOCs attaining the upper bound are given. As consequences, the following new infinite series of optimal (gn 4, 2, 1,)-OOCs are obtained: i) g ∈ {1, 7, 11, 19, 23, 31, 35, 59, 71, 79, 131, 179, 191, 239, 251, 271, 311, 359, 379, 419, 431, 439, 479, 491, 499, 571, 599, 631, 659, 719, 739, 751, 839, 971} or g is a prime 1000 and ≡ 5 (mod 8), and n = 9h 25i 49j p1 p2...pr where h ∈ {0, 1}, i and j are arbitrary nonnegative integers, and each pi is a prime ≡ 1 (mod 8); ii) g = 2g′ where g′ ∈ {1, 7, 11, 19, 23, 31, 47, 71, 127, 151, 167, 191, 263, 271, 311, 359, 367, 383, 431, 439, 463, 479, 503, 631, 647, 719, 727, 743, 823, 839, 863, 887, 911, 919, 967, 983, 991} and n = p1 p2...pr where each pi is a prime ≡ 1 (mod 4); iii) g ∈ {4, 20} and n is any positive integer prime to 30; iv) g = 8 and n = p1 p2...pr where each pi is a prime ≡ 1 (mod 4) greater than 5.