Robert Silverman's research while affiliated with Wright State University and other places

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Publications (3)

A characterization of -stable matrices
Article
  • Feb 2012
In this paper we consider certain (0,1) matrices A of size v×v with exactly k ones in each row and each column where k<v. We say that A is (α,β)-isolated if there is a single zero entry in some α×β submatrix of A. The submatrix need not be contiguous, i.e. formed from α consecutive rows and β consecutive columns of A. A is said to be (α,β)-stable i...
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Incidence matrices with forbidden configurations
Chapter
  • Jan 2010
The objects of our study are certain (0,1)-matrices A of size v×v having exactly k ones in each row and each column where k<v. We say that a zero entry of A is α-isolated if it is the only zero entry in some α×α submatrix of A. The submatrix need not be “contiguous”, i.e., formed from a consecutive rows and a consecutive columns of A. A is said to...
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Maximum distance separable codes and arcs in projective spaces
Article
Full-text available
  • Aug 2007
Given any linear code C over a finite field GF (q) we show how C can be described in a transparent and geometrical way by using the associated Bruen-Silverman code. Then, specializing to the case of MDS codes we use our new approach to offer improvements to the main results currently available concerning MDS extensions of linear MDS codes. We also...
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Citations

... This was essentially proposed by Segre [24] in 1955. MDS Conjecture: If C is a nontrivial linear MDS code of length n and dimension k ≤ q over F q , where q is a power of prime p, then n ≤ q + 1, except when q is even and k = 3 or k = q − 1 in which case n ≤ q + 2. Many papers focus on this conjecture (see for instance, [1,4,25]). The MDS Conjecture has not been proved in general. ...
Reference: Euclidean and Hermitian LCD MDS codes
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