TY - CPAPER
AB - 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 $E := DTIME[2^{O(n)}]$ is not contained in the sub-exponential space class $DSPACE[2^{o(n)}]$. The methods used in this paper are by now standard within computational complexity theory, and the main contribution of this note is observing that they are relevant to the construction of optimal codes. We attempt to make this note self contained, and describe the relevant results and proofs from the theory of pseudorandomness in some detail.
T1 - Computational Hardness and Explicit Constructions of Error Correcting Codes
DA - 2006
AU - Cheraghchi, Mahdi
AU - Shokrollahi, Amin
AU - Wigderson, Avi
JF - Allerton 2006
N1 - Invited paper
ID - 101078
KW - algoweb_coding
KW - algoweb_tcs
UR - http://www.csl.uiuc.edu/allerton/
UR - https://infoscience.epfl.ch/record/101078/files/final.pdf
ER -