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In this paper we give several new constructions of WOM codes. The novelty inour constructions is the use of the so called Wozencraft ensemble of linearcodes. Specifically, we obtain the following results.  We give an explicit construction of a two-write Write-Once-Memory (WOM forshort) code that approaches capacity, over the binary alphabet. More formally,for every \epsilon>0, 0<p<1 and n =(1/\epsilon)^{O(1/p\epsilon)} we give aconstruction of a two-write WOM code of length n and capacityH(p)+1-p-\epsilon. Since the capacity of a two-write WOM code is max_p(H(p)+1-p), we get a code that is \epsilon-close to capacity. Furthermore,encoding and decoding can be done in time O(n^2.poly(log n)) and timeO(n.poly(log n)), respectively, and in logarithmic space.  We obtain a new encoding scheme for 3-write WOM codes over the binaryalphabet. Our scheme achieves rate 1.809-\epsilon, when the block length isexp(1/\epsilon). This gives a better rate than what could be achieved usingprevious techniques.  We highlight a connection to linear seeded extractors for bit-fixing sources.In particular we show that obtaining such an extractor with seed length O(logn) can lead to improved parameters for 2-write WOM codes. We then give anapplication of existing constructions of extractors to the problem of designingencoding schemes for memory with defects.

New constructions of WOM codes using the Wozencraft ensemble