Optical orthogonal codes (OOCs) are sets of $(0,1)$-sequences with good auto- and cross- correlation properties. They were originally introduced for use in multi-access communication, particularly in the setting of optical CDMA communications systems. They can also be formulated in terms of families of subsets of $\Z_v$, where the correlation properties can be expressed in terms of conditions on the internal and external differences within and between the subsets. With this link there have been many studies on their combinatorial properties. However, in most of these studies it is assumed that the auto- and cross-correlation values are equal; in particular, many constructions focus on the case where both correlation values are $1$. This is not a requirement of the original communications application. In this paper, we "decouple" the two correlation values and consider the situation with correlation values greater than $1$. We consider the bounds on each of the correlation values, and the structural implications of meeting these separately, as well as associated links with other combinatorial objects. We survey definitions, properties and constructions, establish some new connections and concepts, and discuss open questions.

翻译：光学正交码（OOC）是具有良好自相关与互相关特性的$(0,1)$序列集合。其最初被提出用于多址通信领域，特别是在光学CDMA通信系统中。这类码也可通过$\Z_v$的子集族进行表述，其相关特性可通过子集内部及子集间的内差与外差条件来描述。基于这一关联，学界已对其组合性质开展了大量研究。然而，在多数现有研究中，通常假设自相关值与互相关值相等；尤其诸多构造方法聚焦于两者均为$1$的情形。但这并非原始通信应用的必要条件。本文通过"解耦"两类相关值，探讨相关值大于$1$的情形。我们分别研究各相关值的理论界限，分析满足不同界限时的结构特性，并建立其与其他组合对象的关联。本文系统梳理了相关定义、性质与构造方法，提出若干新的理论联系与概念框架，并对开放性问题进行探讨。