Article

Designs, Codes and Cryptography

, Volume 58, Issue 1, pp 89-109

First online:

New results on optimal (v, 4, 2, 1) optical orthogonal codes

  • Marco BurattiAffiliated withDipartimento di Matematica e Informatica, Università di Perugia
  • , Koji MomiharaAffiliated withGraduate School of Information Science, Nagoya University
  • , Anita PasottiAffiliated withDipartimento di Matematica, Facoltà di Ingegneria, Università degli Studi di Brescia Email author 

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Abstract

We investigate further the existence question regarding optimal (v, 4, 2, 1) optical orthogonal codes begun in Momihara and Buratti (IEEE Trans Inform Theory 55:514–523, 2009). We give some non-existence results for infinitely many values of v ≡ ± 3 (mod 9) and several explicit constructions for infinite classes of perfect optical orthogonal codes.

Keywords

Optical orthogonal code Difference family Theorem of Weil on multiplicative character sums

Mathematics Subject Classification (2000)

05B30 94B25