Improving the alphabet-size in high noise, almost optimal rate list decodable codes

We revisit the construction of high noise, almost optimal rate list decodable code of Guruswami [1]. Guruswami showed that if one can explicitly construct optimal extractors then one can build an explicit (1 - is an element of, O(1/is an element of)) list decodable codes of rate ohm (is an element of/log 1/is an element of) and alphabet size 2(O(1/is an element of center dot log) (1/is an element of)). We show that if one replaces the expander component in the construction with an unbalanced disperser, then one can dramatically improve the alphabet size to 2(O(log2 1/is an element of)) while keeping all other parameters the same.