AN ALGEBRAIC STUDY OF THE SIMPLEST CODES AND COEFFICIENTLESS EQUATIONS IN WORDS
L G Kiseleva · Mathematics of the USSR-Sbornik · 1980
Let be an alphabet and let be an -code, i.e. a set consisting of words in the alphabet ; let denote the length of a word . Suppose that , that is the alphabet of the message language, and , , , is an alphabetic encoding, characterizes the smallest number of comparisons which are needed to solve the problem of being one-to-one for the -code in the worst case when the size of the input information (the unit of measurement is a comparison of letters from ). It is proved that . We show that a nonhomogeneous equation in words in three unknowns has at most one nontrivial solution, up to isomorphism.Bibliography: 10 titles.