engleski

Construction of self-orthogonal linear codes from orbit matrices of combinatorial structures

The incidence structures can be presented by their incidence matrices. An automorphism group acting on the structure induces the tactical decomposition of the corresponding incidence matrix, from which one can construct the related orbit matrix. We will study codes spanned by the rows of an orbit matrix of a symmetric design with respect to an automorphism group that acts with all orbits of the same length. The dimension of such codes will be discussed. We define an extended orbit matrix and show that under certain conditions the rows of the extended orbit matrix span a code that is self-dual with respect to a certain scalar product. We will also study codes spanned by the rows of the quotient matrices of symmetric (group) divisible designs (SGDD) with the dual property. In a similar way as in the case of symmetric designs, we will discuss self-dual codes constructed from the extended quotient matrices of SGDDs. In adition, we will present a construction of self-orthogonal linear codes from orbit matrices of strongly regular graphs and show that under certain conditions submatrices of orbit matrices of strongly regular graphs span self-orthogonal codes.

self-orthogonal code ; orbit matrix ; combinatorial structure

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