Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771550 | Finite Fields and Their Applications | 2017 | 17 Pages |
Abstract
Given a field F, a scalar λâF and a matrix AâFnÃn, the twisted centralizer code CF(A,λ):={BâFnÃn|ABâλBA=0} is a linear code of length n2 over F. When A is cyclic and λâ 0 we prove that dimâ¡CF(A,λ)=degâ¡(gcdâ¡(cA(t),λncA(λâ1t))) where cA(t) denotes the characteristic polynomial of A. We also show how CF(A,λ) decomposes, and we estimate the probability that CF(A,λ) is nonzero when |F| is finite. Finally, we prove dimâ¡CF(A,λ)⩽n2/2 for λâ{0,1} and 'almost all' nÃn matrices A over F.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Adel Alahmadi, S.P. Glasby, Cheryl E. Praeger,