Constructions of error-correcting DC-free block codes

Two DC-free codes are presented with distance 2d, b>or=1 length 2n+2r(d-1) for d3, where r is the least integer >or=log/sub 2/ (2n+1). For the first code l=4, c=2, and the asymptotic rate of this code is 0.7925. For the second code l=6, c=3, and the asymptotic rate of this code is 0.8858. Asymptotically, these rates achieve the channel capacity. For small values of n these codes do not achieve the best rate. As an example of codes of short length with good rate, the author presents a (30, 10, 6, 4) DC-free block code with 2/sup 21/ codewords. A construction is presented for which from a given code C/sub 1/ of length n, even weight, and distance 4, the author obtains a (4n, l, c, 4) DC-free block code C/sub 2/, where l is 4, 5 or 6, and c is not greater than n+1 (but usually significantly smaller). The codes obtained by this method have good rates for small lengths. The encoding and decoding procedures for all the codes are discussed.>