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- W2963445533 abstract "Given a field F , a scalar λ ∈ F and a matrix A ∈ F n × n , the twisted centralizer code C F ( A , λ ) : = { B ∈ F n × n | A B − λ B A = 0 } is a linear code of length n 2 over F . When A is cyclic and λ ≠ 0 we prove that dim C F ( A , λ ) = deg ( gcd ( c A ( t ) , λ n c A ( λ − 1 t ) ) ) where c A ( t ) denotes the characteristic polynomial of A . We also show how C F ( A , λ ) decomposes, and we estimate the probability that C F ( A , λ ) is nonzero when | F | is finite. Finally, we prove dim C F ( A , λ ) ⩽ n 2 / 2 for λ ∉ { 0 , 1 } and ‘almost all’ n × n matrices A over F ." @default.
- W2963445533 created "2019-07-30" @default.
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- W2963445533 date "2017-11-01" @default.
- W2963445533 modified "2023-09-29" @default.
- W2963445533 title "On the dimension of twisted centralizer codes" @default.
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- W2963445533 doi "https://doi.org/10.1016/j.ffa.2017.07.005" @default.
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