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 − , O(1 )) list decodable codes of rate Ω(log 1 ) and alphabet size 2O( 1 ·log 1 ) . 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 2O(log2 1 ) while keeping all other parameters the same.

• Type: Conference
• Year: 2005
• Where: STACS
• Authors: Eran Rom, Amnon Ta-Shma
• Keywords: Alphabet Size, List Decodable Codes, Optimal Rate List, STACS 2005, Theoretical Computer Science