Asymptotically Optimal Linear Codes Correcting Defects of Linearly Increasing Multiplicity

Asymptotically optimal linear codes are proposed for defect correction. A method of correcting defects of linearly increasing multiplicity $t$ for block length $n\to\infty$ is considered. The method constructs an asymptotically optimal code with redundancy $r(n,t)\sim t$ in polynomial time and requires $O(n\log_2^3 n)$ coding-decoding operations.