What is the maximal cardinality of a subset $A$ of $\{-1,1\}^n$ such that any Hamming sphere with radius $r$ contains at most $k$ elements of $A$?


Are explicit constructions with large cardinality known?
Any relevant comment or reference appreciated.



Large subsets of the Hamming cube with small intersections with all spheres of given radius
Two words: list decoding


Apparently the previous answer is too short to be an answer, so I am writing this sentence.


