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The relation between list decodability of a code and other fundamental parameters such as minimum distance and rate have been fairly well studied. It has been shown that every code can be list decoded using small lists beyond half the minimum distance up to a bound called the Johnson radius.
A linear code of length n and dimension k is a linear subspace C with dimension k of the vector space where is the finite field with q elements. Such a code is called a q -ary code. If q = 2 or q = 3, the code is described as a binary code, or a ternary code respectively. The vectors in C are called codewords.