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Goethals--Seidel difference families with symmetric or skew base blocks. (arXiv:1802.00556v1 [math.CO])
来源于:arXiv
We single out a class of difference families which is widely used in some
constructions of Hadamard matrices and which we call Goethals--Seidel (GS)
difference families. They consist of four subsets (base blocks) of a finite
abelian group of order $v$, which can be used to construct Hadamard matrices
via the well-known Goethals--Seidel array. We consider the special class of
these families in cyclic groups, where each base block is either symmetric or
skew. We omit the well-known case where all four blocks are symmetric. By
extending previous computations by several authors, we complete the
classification of GS-difference families of this type for odd $v<50$. In
particular, we have constructed the first examples of so called good matrices,
G-matrices and best matrices of order 43, and good matrices and G-matrices of
order 45. We also point out some errors in one of the cited references. 查看全文>>