Designs, Codes and Cryptography

, Volume 58, Issue 1, pp 89–109

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

Article

DOI: 10.1007/s10623-010-9382-z

Cite this article as:
Buratti, M., Momihara, K. & Pasotti, A. Des. Codes Cryptogr. (2011) 58: 89. doi:10.1007/s10623-010-9382-z

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 codeDifference familyTheorem of Weil on multiplicative character sums

Mathematics Subject Classification (2000)

05B3094B25

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità di PerugiaPerugiaItaly
  2. 2.Graduate School of Information ScienceNagoya UniversityNagoyaJapan
  3. 3.Dipartimento di Matematica, Facoltà di IngegneriaUniversità degli Studi di BresciaBresciaItaly