As discussed in "Word Arithmetic" in the November 1996 Word Ways, there are two ways to construct difference words. The first was examined in detail in "Absolute Difference Words" in February; the second is the subject of this article. Briefly, a cyclic difference word is formed form a source word such as VASE (188.8.131.52) by subtracting the ith number from the (i+1)st, if necessary adding 26 to the latter to make them different positive (5 = 27.22, 18 = 19-1 = 31-19, yielding the target word ERL).
"Cyclic Difference Words,"
Word Ways: Vol. 30
, Article 16.
Available at: https://digitalcommons.butler.edu/wordways/vol30/iss2/16