Abstract
In this paper, by applying the precoding technique in conjunction with the syndrome compression approach, we construct systematic t -deletion s -substitution correcting codes, where t and s are fixed positive integers. The redundancy of our construction is (4t+3s)\log n+o(\log n) for the binary case and (4t+4s-1- \mathrm{L}\frac{2s-1}{q}\rfloor)\bar{\mathrm{l}}\text{og}_{q}n+o(\bar{\mathrm{l}}\text{og}_{q}n) for the q -ary case, where n is the length of the codes and q> 2 is a fixed prime power. 1 1 If x is a positive real number, then \log_{q}\alpha is the logarithm of x with base q ; if q=2 , we simply denote \log x=\text{lo}\bar{\mathrm{g}}_{q}x . We also construct binary t-deletion correcting codes (i.e., s=0 ) with redundancy (4t-1)\log n+o(\log n) . The encoding/decoding complexities of all constructions are polynomial in n .