Lexicographic codes or lexicodes are greedily generated error-correcting codes with remarkably good properties. They were produced independently by Levenshtein and Conway and Sloane  and are known to be linear over some finite fields.
A lexicode of minimum distance d and length n over a finite field is generated by starting with the all-zero vector and iteratively adding the next vector (in lexicographic order) of minimum Hamming distance d from the vectors added so far. As an example, the length-3 lexicode of minimum distance 2 would consist of the vectors marked by an "X" in the following example:
Vector In code? 000 X 001 010 011 X 100 101 X 110 X 111
- V.I. Levenstein. A class of systematic codes. Soviet Math. Dokl, 1(1):368-371, 1960.
- J.H. Conway and N.J.A Sloane. Lexicographic codes: error-correcting codes from game theory. IEEE Transactions on Information Theory, 32:337-348, 1986.
- Ari Trachtenberg, Designing Lexicographic Codes with a Given Trellis Complexity, IEEE Transactions on Information Theory, January 2002.
- Bob Jenkins table of binary lexicodes
- On-line generator for lexicodes and their variants
- "Sloane's A075928 : List of codewords in binary lexicode with Hamming distance 4 written as decimal numbers.". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- Error-Correcting Codes on Graphs: Lexicodes, Trellises and Factor Graphs