Computational Hardness and Explicit Constructions of Error Correcting Codes (original) (raw)

We outline a procedure for using pseudorandom generators to construct binary codes with good properties, assuming the existence of sufficiently hard functions. Specifically, we give a polynomial time algorithm, which for every integers n and k, constructs polynomially many linear codes of block length n and dimension k, most of which achieving the Gilbert-Varshamov bound. The success of the procedure relies on the assumption that the exponential time class of E def = DTIME[2 O(n) ] is not contained in the sub-exponential space class DSPACE[2 o(n) ].