Unified combinatorial constructions of optimal optical orthogonal codes

Cuiling Fan; Koji Momihara

doi:10.3934/amc.2014.8.53

Article Contents

2014, Volume 8, Issue 1: 53-66. Doi: 10.3934/amc.2014.8.53

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Unified combinatorial constructions of optimal optical orthogonal codes

Cuiling Fan^1, and
Koji Momihara^2,

1.
Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027
2.
Faculty of Education, Kumamoto University, 2-40-1 Kurokami, Kumamoto 860-8555

Received: May 2012

Revised: June 2013

Published: February 2014

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Abstract

We present unified constructions of optical orthogonal codes (OOCs) using other combinatorial objects such as cyclic linear codes and frequency hopping sequences. Some of the obtained OOCs are optimal or asymptotically optimal with respect to the Johnson bound. Also, we are able to show the existence of new optimal frequency hopping sequences (FHSs) with respect to the Singleton bound from our observation on a relation between OOCs and FHSs. The last construction is based on residue rings of polynomials over finite fields, and it yields a new large class of asymptotically optimal $(q-1,k,k-2)$-OOCs for any prime power $q$ with $\gcd{(q-1,k)}=1$. Some infinite families of optimal ones are included as a subclass.

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Mathematics Subject Classification: Primary: 94B25; Secondary: 05B40.

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