… Our goal is to construct a linear code of labelings of the vertices in a Johnson graph such …
a neighborhood in the graph. In this section we formulate the requirements for the code. In the …

… We consider the Johnson graph J(~,w), 0 < w < n. The graph has (E) vertices representing
the (z) w-subsets of an n-set. Two vertices are connected by an edge if the intersection …

… codes in Johnson graphs, and our focus in this paper is on a related family of codes in these
graphs … Completely regular codes in Johnson graphs have been studied by Meyerowitz [18, …

… codes with sum-product decoding is the girth of the code. The girth of an LDPC code is
defined as the girth of the incidence graph … As the incidence graph (also called a Tanner graph …

… More formally, for the 7-bit ASCII plus even parity code we define a codeword c to have the
… use a new LDPC code with Tanner graph shown in Fig. 2.3. For this Tanner graph there is a 4…

… To date, randomly constructed LDPC codes have largely relied on … graph. A key idea in
this paper is that cycles of length less than 6 in the Tanner graph associated with an LDPC code …

… codes in the Johnson graphs such that all codewords are equivalent and also all code-…
symmetries of the code, that is to say, the study of neighbour-transitive codes. Our approach is in …

… codes in Johnson graphs, the problem of existence of block schemes, the problem of existence
of completely regular codes in Johnson graphs … in other graphs, are given in this paper. …

… graph isomorphism testing2. Our focus in this paper is studying Johnson graphs as ‘carrier
spaces’ of errorcorrecting codes … of examples of codes and designs with ‘high symmetry’. The …

… the binary codes generated by the row span of adjacency matrices of the uniform subset
graph (2 , ,1) kk G and the Johnson graph (2 , , 1) kkk G - coincide despite the graphs being non-…