一种无排列的长度为3的十进制校验位码
A Permutation-Free Length 3 Decimal Check Digit Code
AI总结：
本文构造了一种长度为3的十进制校验位码，任意两位数字即可确定整个码字，从而消除循环错误和语音错误。
摘要：
1969年，J. Verhoeff首次给出了使用单个校验位来防范所有单错、换位错和相邻孪生错的十进制检错码示例。他提出的三种码都是长度为3位、含2个信息位的码。若存在4位码，则意味着存在10个互不相交的3位码。显然，目前甚至不知道是否存在一对这样的互不相交的3位码。本文所构造的码具有如下性质：即使不知道任意两位数字的位置，只要知道这两个数字就足以确定整个码字。这实现了Verhoeff消除“循环错误”的愿望。语音错误，即形如X0和1X的两位数字对被互换的情况，也被消除了。
英文摘要：
In 1969 J. Verhoeff provided the first examples of a decimal error detecting code using a single check digit to provide protection against all single, transposition and adjacent twin errors. The three codes he presented are length 3-digit codes with 2 information digits. Existence of a 4-digit code would imply the existence of 10 such disjoint 3-digit codes. Apparently, not even a pair of such disjoint 3-digit codes is known. The code developed herein, has the property that the knowledge of any two digits is sufficient to determine the entire codeword even though their positions were unknown. This fulfills Verhoeff's desire to eliminate "cyclic errors". Phonetic errors, where 2 digit pairs of the forms X0 and 1X are interchanged, are also eliminated.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
