A Lower Bound on List Size for List Decoding

A q-ary error-correcting code C {1,2,...,q}n is said to be list decodable to radius with list size L if every Hamming ball of radius contains at most L codewords of C. We prove that in order for a q-ary code to be list-decodable up to radius (1 1/q)(1 )n, we must have L = (1/ 2). Specically, we prove that there exists a ..