Construction of self-orthogonal codes from combinatorial designs
Consider binary linear codes generated by matrices of the form \([I\;A]\), where \(I\) is an identity matrix. Self-orthogonal such codes can be obtained by letting \(A\) be a part (obtained by removing some rows, if necessary) of the incidence matrix of a \(2\)-\((v,k,\lambda)\) BIBD for certain sets of parameters. There is also another variant of this construction that gives self-orthogonal codes. The authors construct codes via a classification of the matrices \(A\), that is, parts of BIBDs with given small parameters. Well-established techniques are used in this classification. The number of isomorphism classes of codes obtained in this manner as well as the minimum distance of the codes are tabulated for 13 sets of parameters of the underlying BIBD.
scientific article; zbMATH DE number 6121281