Title :
On the Size of Optimal Three-Error-Correcting Binary Codes of Length 16
Author :
Östergård, Patric R J
Author_Institution :
Dept. of Commun. & Networking, Aalto Univ., Aalto, Finland
Abstract :
Let A(n,d) denote the maximum size of a binary code with length n and minimum distance d. It has been known for decades that A(16,7) = A(17,8) = 36 or 37, that is, that the size of optimal 3-error-correcting binary codes of length 16 is either 36 or 37. By a recursive classification via subcodes and a clique search in the final stage, it is shown that the size of optimal such codes is 36.
Keywords :
binary codes; error correction codes; recursive estimation; search problems; clique search; length 16; optimal three-error-correcting binary codes; recursive classification; Algorithm design and analysis; Binary codes; Computers; Educational institutions; Linear programming; Upper bound; Bounds on codes; code equivalence; error-correcting code; linear programming; optimal code;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2011.2144955
