Generators for primary closures of Galois fields.

DOI10.1016/S1071-5797(02)00021-7zbMath1075.11080MaRDI QIDQ1867485

Dirk Hachenberger

Publication date: 2 April 2003

Published in: Finite Fields and their Applications (Search for Journal in Brave)

zbMATH Keywords

normtracenormal basisprimitive elementcompletely normal (completely free) elementfinite (Galois) fieldnormal (free) elementtrace-compatible sequencenorm-compatible sequenceuniversal quadruple

Mathematics Subject Classification ID

Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30)

Related Items (4)

Primitive complete normal bases: existence in certain 2-power extensions and lower bounds ⋮ Characterizing Normal Bases via the Trace Map ⋮ Explicit theorems on generator polynomials ⋮ Further results on the Morgan-Mullen conjecture

Cites Work

• Primitive elements and polynomials with arbitrary trace
• Primitive normal bases with prescribed trace
• Primitive normal bases for towers of field extensions
• Primitivity, freeness, norm and trace
• Bases for finite fields and a canonical decomposition for a normal basis generator
• Characterizing Normal Bases via the Trace Map
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