#18714: Dual bases for finite fields
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Reporter: tgagne | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-6.8
Component: finite rings | Keywords: dual basis, finite field
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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The dual basis `d` of a basis `e` of the finite field `GF(p)^n` has the
property that the field trace of the product of an element of `e` with an
element of `d` equals the Kronecker delta function. Every linear function
over `GF(p)^n` can be realized as a polynomial over `GF(p^n)`; the dual
basis is critical to the determination of this polynomial.
The algorithm for dual basis calculation comes from pages 110-111 of
!McEliece's "Finite Fields for Computer Scientists and Engineers" and is
calculated with a single matrix inversion over `GF(p)`.
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Ticket URL: <http://trac.sagemath.org/ticket/18714>
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