Optimal Codes With Small Constant Weight in ℓ₁-Metric.

Motivated by the duplication-correcting problem for data storage in live DNA, we study the construction of constant-weight codes in ℓ1-metric. By using packings and group divisible designs in combinatorial design theory, we give constructions of optimal codes over non-negative integers and optimal ternary codes with ℓ1-weight w ≤ 4 for all possible distances. In general, we derive the size of the largest ternary code with constant weight w and distance 2w−2 for sufficiently large length n satisfying n ≡ 1, w, −w+2,−2w+3 (mod w(w−1)). [ABSTRACT FROM AUTHOR]