The covering radius of extreme binary 2-surjective codes.

The covering radius of binary 2-surjective codes of maximum length is studied in the paper. It is shown that any binary 2-surjective code of M codewords and of length $$n = {M-1 \choose \left\lfloor(M-2)/2\right\rfloor}$$ has covering radius $$\frac{n}{2} - 1$$ if M - 1 is a power of 2, otherwise $$\left\lfloor\frac{n}{2}\right\rfloor$$ . Two different combinatorial proofs of this assertion were found by the author. The first proof, which is written in the paper, is based on an existence theorem for k-uniform hypergraphs where the degrees of its vertices are limited by a given upper bound. The second proof, which is omitted for the sake of conciseness, is based on Baranyai’s theorem on l-factorization of a complete k-uniform hypergraph. [ABSTRACT FROM AUTHOR]