### Abstract

We show that for any fixed prime q ≥ 5 and constant ζ > 0, it is NP-hard to distinguish whether a two prove one round game with q ^{6} answers has value at least 1-ζ or at most 4/q. The result is obtained by combining two techniques: (i) An Inner PCP based on the point versus subspace test for linear functions. The testis analyzed Fourier analytically. (ii) The Outer/Inner PCP composition that relies on a certain sub-code covering property for Hadamard codes. This is a new and essentially black-box method to translate a codeword test for Hadamard codes to a consistency test, leading to a full PCP construction. As an application, we show that unless NP has quasi-polynomial time deterministic algorithms, the Quadratic Programming Problem is in approximable within factor (log n) ^{1/6 - o(1)}.

Original language | English (US) |
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Title of host publication | Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 |

Pages | 648-657 |

Number of pages | 10 |

DOIs | |

State | Published - Dec 1 2011 |

Event | 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 - Palm Springs, CA, United States Duration: Oct 22 2011 → Oct 25 2011 |

### Publication series

Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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ISSN (Print) | 0272-5428 |

### Other

Other | 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011 |
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Country | United States |

City | Palm Springs, CA |

Period | 10/22/11 → 10/25/11 |

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### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011*(pp. 648-657). [6108226] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS). https://doi.org/10.1109/FOCS.2011.62