Orphan structure of the first-order Reed-Muller codes

Richard A. Brualdi, Ning Cai, Vera S. Pless
1992 Discrete Mathematics  
Brualdi, R.A., N. Cai and VS. Pless, Orphan structure of the first-order Reed-Muller codes, Discrete Mathematics 102 (1991) 239-247. We investigate a method of combining two codes which we call the outer product. First-order Reed-Muller codes are outer products of a number of copies of the full binary space of length 2, and we apply our results to obtain cosets of the Reed-Muller codes which have no ancestors, that is, which are orphans.
doi:10.1016/0012-365x(92)90118-y fatcat:ldwuv7uotbfltgmqq2f73mmmg4