Advances in Mathematics of Communications (AMC)

Unified combinatorial constructions of optimal optical orthogonal codes

Pages: 53 - 66, Volume 8, Issue 1, February 2014      doi:10.3934/amc.2014.8.53

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Cuiling Fan - Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, China (email)
Koji Momihara - Faculty of Education, Kumamoto University, 2-40-1 Kurokami, Kumamoto 860-8555, Japan (email)

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.

Keywords:  Optical orthogonal code, cyclic linear code, frequency hopping sequence.
Mathematics Subject Classification:  Primary: 94B25; Secondary: 05B40.

Received: May 2012;      Revised: June 2013;      Available Online: January 2014.