منابع مشابه
The superregular graphs
A regular graph is superregular if it has no vertices or if the subgraphs induced by the neighbors and by the nonneighbors of each vertex are superreg-ular. The superregular graphs are precisely the disjoint union of m isomorphic cliques, the Cartesian product of two isomorphic cliques, the ve-cycle, and the complements of these graphs.
متن کاملOn superregular matrices and MDP convolutional codes
Superregular matrices are a type of lower triangular Toeplitz matrix that arises in the context of constructing convolutional codes having a maximum distance profile. These matrices are characterized by the property that the only submatrices having a zero determinant are those whose determinants are trivially zero due to the lower triangular structure. In this paper, we discuss how superregular...
متن کاملSuperregular matrices and applications to convolutional codes
The main results of this paper are twofold: the first one is a matrix theoretical result. We say that a matriz is superregular if all of its minors that are not trivially zero are nonzero. Given a a × b, a ≥ b, superregular matrix over a field, we show that if all of its rows are nonzero then any linear combination of its columns, with nonzero coefficients, has at least a − b + 1 nonzero entrie...
متن کاملA new class of superregular matrices and MDP convolutional codes
This paper deals with the problem of constructing superregular matrices that lead to MDP convolutional codes. These matrices are a type of lower block triangular Toeplitz matrices with the property that all the square submatrices that can possibly be nonsingular due to the lower block triangular structure are nonsingular. We present a new class of matrices that are superregular over a sufficien...
متن کاملSuperregular Matrices and the Construction of Convolutional Codes having a Maximum Distance Profile
Superregular matrices are a class of lower triangular Toeplitz matrices that arise in the context of constructing convolutional codes having a maximum distance profile. These matrices are characterized by the property that no submatrix has a zero determinant unless it is trivially zero due to the lower triangular structure. In this paper, we discuss how superregular matrices may be used to cons...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1979
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1979.84.465