Global ETD Search
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Showing 1 to 2 of 2 for “"field of two elements"”.
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On Dihedral Codes and the Double Circulant Conjecture for Binary Extended Quadratic Residue Codes
… F2[x]/⟨1 + xk⟩ where F2 is the Galois field of two elements. We identify the binary extended quadratic residue codes of length 2k as principal left ideals in the group algebra F2Dk where Dk is the dihedral group of order 2 k. We prove that these codes have a double circulant …
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The Minimum Rank Problem Over Finite Fields
We have two main results. Our first main result is a sharp bound for the number of vertices in a minimal forbidden subgraph for the graphs having minimum rank at most 3 over the finite field of order 2. We also list all 62 such minimal forbidden subgraphs and show that many of these are minimal …