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In this paper we give an explicit construction of a capacity achieving familyof binary t-write WOM codes for any number of writes t, that have a polynomialtime encoding and decoding algorithms. The block length of our construction isN=(t/\epsilon)^{O(t/(\delta\epsilon))} when \epsilon is the gap to capacity andencoding and decoding run in time N^{1+\delta}. This is the first deterministicconstruction achieving these parameters. Our techniques also apply to largeralphabets.

Capacity achieving multiwrite WOM codes