Suppose that L is a nonempty language over A, \(k\in \mathbb {N}^0\) and \(m\in \mathbb {N}\). If L satisfies \((LA^k)^mL\)\(\cap A^+(LA^k)^{m-1}LA^+=\emptyset \), then L is a code and is called a (k, m)-comma code. If L is a (k, m)-comma code, then it is known that L is an infix code when \(m=1\) and L is a bifix code when \(m\ge 1\). In this paper, we extend the study and find that the class of (k, m)-comma codes and the class of infix codes are incomparable but they are not disjoint, so we first characterize the (k, m)-comma codes with \(m\ge 2\) which are infix codes. We also describe the solid codes with minimum lengths greater than k and the 2-(k, 1)-comma codes by different approaches. Finally, the class of bifix codes will be classified into disjoint union of some subclasses and a criterion to determine the subclass membership of a given bifix code will be given.

中文翻译：

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$$ {（\ varvec {k，m}）} $$（k，m）-逗号代码的一些结果

假设L是A，\（k \ in \ mathbb {N} ^ 0 \）和\（m \ in \ mathbb {N} \）上的非空语言。如果L满足\（（LA ^ k）^ mL \）\（\ cap A ^ +（LA ^ k）^ {m-1} LA ^ + = \ emptyset \），则L是一个代码，称为a （k，  m）-逗号代码。如果大号是（ķ， 米）-comma代码，那么，已知大号是缀代码时\（M = 1 \）和大号是bifix代码时\（米\ GE 1 \） 。在本文中，我们扩展了研究，发现（k，  m）-逗号代码和中缀代码的类是不可比的，但它们不是相交的，因此我们首先用\（m \ ge 2 \）来表征（k，  m）逗号代码，它们是中缀代码。我们还通过不同的方法描述了最小长度大于k的实心代码和2-（k，1）逗号代码。最后，bifix代码的类别将被分类为某些子类的不交集并给出确定给定bifix代码的子类成员资格的标准。