A note on the equivalence between strict optical orthogonal codes and difference triangle sets

Zhang (see IEEE Trans. Commun., vol.47, p.967-973, July 1999) proposed a special family of optical address codes, called strict optical orthogonal codes (S-OOCs), was proposed for fiber-optic code-division multiple-access (FO-CDMA) networks. Such codes can strictly guarantee both cross-correlation and autocorrelation functions constrained to have the value one in fully asynchronous data communications and ultra fast switching. In Zhang´s work the theory and designs of S-OOC, plus several examples, comparison tables, and performance analyses were presented. In this article, we set up the equivalence between S-OOC and so-called difference triangle sets (DTS), which have been extensively studied previously. Thus, all the known constructions, bounds, and analyses for DTS can be directly applied to S-OOC.