Minimal-change order and separability in linear codes

A linear code E? is said to he in minimal-change order if each codeword differs from its predecessor by a word of minimum weight. A rule is presented to construct such an order in case that i? has a basis of codewords with minimum weight. Some consequences concem-ing the ranking and separability in 5 F are mentioned. It is well known that the set of all binary words of length n can be ordered in a list such that each word differs from its predecessor by precisely 1 bit. Such a list is called a Gray code. For any value of n, there are many such lists possible. The best known example is the so-called binary rejlected or normal Gray code (cf. [3, pp. 172-1771]. We denote this code by the matrix r 1 (1) (2) and (3) solve the ranking problem of G(n). A related question in this context is the separabilityproblem. If two codewords g, and gl have Hamming distance m, one can ask how they are located with respect to each other in the ordered list G(n) or, more specifically, one can ask for bounds for their Gray distance Ii-jl.