Analogously to de Bruijn sequences, Orientable sequences have application in automatic position-location applications and, until recently, studies of these sequences focused on the binary case. In recent work by Alhakim et al., recursive methods of construction were described for orientable sequences over arbitrary finite alphabets, requiring 'starter sequences' with special properties. Some of these methods required as input special orientable sequences, i.e. orientable sequences which were simultaneously negative orientable. We exhibit methods for constructing special orientable sequences with properties appropriate for use in two of the recursive methods of Alhakim et al. As a result we are able to show how to construct special orientable sequences for arbitrary sizes of alphabet (larger than a small lower bound) and for all window sizes. These sequences have periods asymptotic to the optimal as the alphabet size increases.

翻译：类似于德布鲁因序列，可定向序列在自动定位应用中具有用途，且直到最近，相关研究主要集中于二进制情形。在Alhakim等人的近期工作中，描述了针对任意有限字母表上可定向序列的递归构造方法，这些方法需要具备特殊性质的"起始序列"。其中部分方法要求输入特殊可定向序列，即同时满足负可定向性质的可定向序列。我们提出了构造特殊可定向序列的方法，这些序列具备适用于Alhakim等人两种递归方法的特性。结果表明，我们能够构造适用于任意字母表规模（超过较小下界）及所有窗口尺寸的特殊可定向序列。随着字母表规模增大，这些序列的周期渐近趋于最优值。