Disproof of a conjecture on the existence of balanced optimal covering codes
P. Östergård · IEEE Transactions on Information Theory · 2003
The minimum number of codewords in a binary code with length n and covering radius R is denoted by K(n,R), and corresponding codes are called optimal. A code with M words is said to be balanced in a given coordinate if the number of 0's and 1's in this coordinate are at least /spl lfloor/M/2/spl rfloor/. A code is balanced if it is balanced in all coordinates. It has been conjectured that among optimal covering codes with given parameters there is at least one balanced code. By using a computational method for classifying covering codes, it is shown that there is no balanced code attaining K(9,1)=62.