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On optimal (v, 5, 2, 1) optical orthogonal codes

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Abstract

The size of a (v, 5, 2, 1) optical orthogonal code (OOC) is shown to be at most equal to \({\lceil{\frac{v}{12}}\rceil}\) when v ≡ 11 (mod 132) or v ≡ 154 (mod 924), and at most equal to \({\lfloor{\frac{v}{12}}\rfloor}\) in all the other cases. Thus a (v, 5, 2, 1)-OOC is naturally said to be optimal when its size reaches the above bound. Many direct and recursive constructions for infinite classes of optimal (v, 5, 2, 1)-OOCs are presented giving, in particular, a very strong indication about the existence of an optimal (p, 5, 2, 1)-OOC for every prime p ≡ 1 (mod 12).

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Perugia, Via Vanvitelli 1, 06123, Perugia, Italy

    Marco Buratti

  2. Dipartimento di Matematica, Facoltà di Ingegneria, Università degli Studi di Brescia, Via Valotti 9, 25133, Brescia, Italy

    Anita Pasotti

  3. Department of Mathematics, Guangxi Normal University, 541004, Guilin, People’s Republic of China

    Dianhua Wu

Authors
  1. Marco Buratti
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  2. Anita Pasotti
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  3. Dianhua Wu
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Correspondence to Marco Buratti.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Finite Geometries”.

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Buratti, M., Pasotti, A. & Wu, D. On optimal (v, 5, 2, 1) optical orthogonal codes. Des. Codes Cryptogr. 68, 349–371 (2013). https://doi.org/10.1007/s10623-012-9654-x

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  • DOI: https://doi.org/10.1007/s10623-012-9654-x

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