In many cases, it is impossible for a decoding algorithm to specify a unique codeword closest to a received word; list decoding refers to the technique of producing a short list of possible codewords. The key concept is (e,ℓ)-list decodability, which is when every Hamming ball of radius e contains at most ℓ codewords. The interest is in determining A’(n,d,e), that is, the smallest ℓ for which every binary code of length n and dimension d is (e,ℓ)-list decodable.
This paper determines A’(n,d,e) for all e < 4 (the “small radii” in the title) for all but 42 values of n. These 42 lacunae are due to unanswered questions about A(n,d,e), the maximum size of an (n,d,e) constant-weight code--that is, an (n,d) code, all of whose codewords have Hamming weight e.
The paper has comprehensive tables, but no new techniques are presented.