Guest column: inapproximability results via Long Code based PCPs
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Let P 1 be any fixed real. We show that assuming NP 驴 RP, it is hard to approximate the Shortest Vector Problem (SVP) in 驴_p norm within an arbitrarily large constant factor. Under the stronger assumption NP 驴 RTIME^(2^poly(logn)), we show that the problem is hard to approximate within factor 2^{(\log n){1 \mathord{\left/ {\vphantom {1 {2 -\varepsilon }}} \right. \kern-\nulldelimiterspace} {2 -\varepsilon }}} where n is the dimension of the lattice and 驴 0 is an arbitrarily small constant. This greatly improves all previous results in 驴_p norms with 1