Maximum subset of words with Hamming distance ≥ D For all words of fixed length L over a given alphabet, I am interested in a practical algorithm that can give me a subset of maximal cardinality such that the Hamming distance between any two words in the subset equals D. 
(The following variation is also of great interest: ... Hamming distance between any two words in the subset is at least D.)

Is there a mathematical result about the cardinality of such sets, depending on the alphabet, the length L of the words, and the minimum distance D?

Thank you very much.
In coding theory, the quantity you are looking for is called $A_q(n, d)$, where $n$ is the length of vectors, $d$ is the minimum distance between them, and $q$ is the alphabet size (omitted when $q=2$). Characterizing $A_q(n,d)$ is a challenging open problem (with many basic questions remaining unanswered) but various asymptotic and non-asymptotic upper and lower bounds are known. See Chapter 17 of the book "The Theory of Error-Correcting Codes" by MacWilliams and Sloane for a summary of the most important ones.