On unordered codes

By extending the results obtained by D. E. Knuth (1986), a parallel unordered coding scheme with 2^r information bits is described. Balanced codes in which each codeword contains equal amounts of zeros and ones, with r check bits and up to 2^r+1-(r+2) information bits, are constructed. Unordered codes with r check bits and up to 2^r+2^r-1-1 information bits are designed. Codes capable of detecting 2^r-1+[2^r/2]-1 unidirectional errors using r check bits are also described. A review of previous work is presented