Minimum distance bounds for s-regular codes
A code C subset of or equal to F-n is s-regular provided, for every vertex x is an element of F-n, if x is at distance at most s from C then the number of codewords y is an element of C at distance i from x depends only on i and the distance from x to C. If rho denotes the covering radius of C and C is rho -regular, then C is said to be completely regular. Suppose C is a code with minimum distance d, strength t as an orthogonal array, and dual degree s*. We prove that d less than or equal to 2t + 1 when C is completely regular (with the exception of binary repetition codes). The same bound holds when C is (t + 1)-regular. For unrestricted codes, we show that d less than or equal to s* + t unless C is a binary repetition code.
error-correcting codes fundamental parameters completely regular codes hamming graph