2020/04/06 by Tsuyoshi Miezaki, Miezaki, Tsuyoshi, Hiroyuki Nakasora +1
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Cellular Automata and Applications
paper · pdf · doi:10.48550/arxiv.2004.03396
We previously proposed the first nontrivial examples of a code having support t-designs for all weights obtained from the Assmus-Mattson theorem and having support t'-designs for some weights with some t'>t. This suggests the possibility of generalizing the Assmus-Mattson theorem, which is very important in design and coding theory. In the present paper, we generalize this example as a strengthening of the Assmus-Mattson theorem along this direction. As a corollary, we provide a new characterization of the extended Golay code G24.