Difference sets over Galois rings with odd extension degrees and characteristic an even power of 2
M Yamada - Designs, codes and cryptography, 2013 - Springer
M Yamada
Designs, codes and cryptography, 2013•SpringerWe construct an infinite family of (2 ns, 2 ns/2-1 (2 ns/2− 1), 2 ns/2-1 (2 ns/2-1− 1)) difference
sets over a Galois ring GR (2 n, s) with characteristic an even power n of 2 and an odd
extension degree s. It makes a chain of difference sets preserving the structures when n
increases and s is fixed. We introduce a new operation into GR (2 n, s). The Gauss sum
associated with the multiplicative character defined by the subgroup with respect to the new
operation plays an important role in the construction.
sets over a Galois ring GR (2 n, s) with characteristic an even power n of 2 and an odd
extension degree s. It makes a chain of difference sets preserving the structures when n
increases and s is fixed. We introduce a new operation into GR (2 n, s). The Gauss sum
associated with the multiplicative character defined by the subgroup with respect to the new
operation plays an important role in the construction.
Abstract
We construct an infinite family of (2 ns , 2 ns/2 -1(2 ns/2−1), 2 ns/2 -1(2 ns/2 -1 −1)) difference sets over a Galois ring GR(2 n , s) with characteristic an even power n of 2 and an odd extension degree s. It makes a chain of difference sets preserving the structures when n increases and s is fixed. We introduce a new operation into GR(2 n , s). The Gauss sum associated with the multiplicative character defined by the subgroup with respect to the new operation plays an important role in the construction.
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