Lower bounds on the minimum hamming distance achievable with runlengh constrained or DC free block codes and the synthesis of a (16,8) Dmin= 4 DC free block code

Error correction coding gain can be obtained with dc free magnetic recording codes having a minimum Hamming distance
d_{\min}\geq 4
. In this information theoretic paper we establish lower bounds on the minimum Hamming distance achievable with (2n,k) (ie R = k/2n) block codes with runlength constrained or dc free sequences, and present a table with the computed guaranteed minimum values of k for (2n,k) dc free block codes with (b=0, l=2n-1, C=n) sequences, a specified block length 2n and desired minimum Hamming distance
d_{\min}
. Subsequently, we present the formal synthesis of a (16,8)
d_{\min}=4
code with sequences which have, in NRZ notation, a minimum runlength of 1 and maximum runlength of 8, while the bound on the maximum instantaneous accumulated charge is C = 5. This accumulated charge returns to zero at the end of each 16 bit code word. Encoding and decoding schemes for the synthesized code are also proposed.