Disjoint difference sets with regard to the largest elements are used to construct multiple-burst error-correcting codes using majority-logic decoding. Almost all of D.M. Mandelbaum's (1972) codes are improved with shorter lengths. Because they are quasi-cyclic and majority-logic decodable, they are of practical interest.>

Disjoint difference sets (DDS), difference triangle sets (DTS), and related codes are discussed and a recursive construction for DDS is given. With this construction and the relationship between DDS and DTS, many new upper bounds for DTS and some better orthogonal codes are obtained.>

A new binary (22,13,5) quasi-perfect code is presented. The weight distributions of the coset codes are given. The code obtained is not equivalent to T.J. Wagner's code (1966). Four lower bounds for constant weight codes can be derived from it, which are better than the codes with the same parameters in R.L. Graham and N.J. Sloane (1980) and A.E. Brouwer et al. (1980).>

A lower bound on the length of binary self-orthogonal unequal error protection (UEP) codes is derived, and two design procedures for constructing optimal self-orthogonal UEP codes are proposed. With this lower bound, known self-orthogonal UEP codes can be evaluated. It is pointed out that, for given values of minimum distance and code rate, the self-orthogonal codes must be relatively long, so optimal self-orthogonal codes are not optimal in general. But self-orthogonal codes can be implemented simply, and they have error-correcting capabilities beyond those guaranteed by their minimum distance. These properties can be viewed as a partial compensation for using self-orthogonal codes.>