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− 2, O( 1 2 )) list decodable codes of rate Ω( 2 log 1 2 ) and alphabet size 2 1 2 ·log 1 2 . 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 2 1 2 ) while keeping all other parameters the same.