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OOCs, Partial Relative Difference Families and a Conjecture of Golomb

Omrani, Reza and Kumar, Vijay P and Moreno, Oscar and Golomb, Solomn W (2006) OOCs, Partial Relative Difference Families and a Conjecture of Golomb. In: IEEE International. Symposium on .Inform Theory 2006, , 9-14 July 2006 , Seattle, WA.

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The cyclic difference sets constructed by Singer are also examples of perfect distinct difference sets (DDS). The Bose construction of distinct difference sets, leads to a relative difference set. In this paper we introduce the concept of partial relative DDS and prove that an optical orthogonal code (OOC) construction due to Moreno et. al., is a partial relative DDS. We generalize the concept of ideal matrices previously introduced by Kumar and relate it to the concepts of this paper. Another variation of ideal matrices is introduced in this paper: Welch ideal matrices of dimension n by (n - 1). We prove that Welch ideal matrices exist only for n prime. Finally, we recast an old conjecture of Golomb on the Welch construction of Costas arrays using the concepts of this paper. This connection suggests that our construction of partial relative difference sets is in a sense, unique

Item Type: Conference Paper
Publisher: IEEE
Additional Information: Copyright 2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 10 Nov 2011 04:39
Last Modified: 10 Nov 2011 04:39
URI: http://eprints.iisc.ac.in/id/eprint/42022

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