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• W1976720753 abstract "This paper presents procedures for constructing irreducible polynomials over GF ( 2 s ) with linearly independent roots (or normal polynomials or N -polynomials). For a suitably chosen initial N -polynomial F 0 ( x ) ∈ GF ( 2 s ) of degree n , polynomials F k ( x ) ∈ GF ( 2 s ) of degrees n 2 k are constructed by iteratively applying the transformation x → x + x - 1 , and their roots are shown to form a normal basis of GF ( 2 sn 2 k ) over GF ( 2 s ) . In addition, the sequences are shown to be trace compatible , i.e., the trace map T GF ( 2 sn 2 k + 1 ) / GF ( 2 sn 2 k ) from GF ( 2 sn 2 k + 1 ) onto GF ( 2 sn 2 k ) maps the roots of F k + 1 ( x ) onto those of F k ( x ) ." @default.
• W1976720753 created "2016-06-24" @default.
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• W1976720753 date "2008-05-01" @default.
• W1976720753 modified "2023-09-29" @default.
• W1976720753 title "Recursive constructions of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:mi>N</mml:mi></mml:math>-polynomials over <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si2.gif overflow=scroll><mml:mtext>GF</mml:mtext><mml:mo stretchy=false>(</mml:mo><mml:msup><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msup><mml:mo stretchy=false>)</mml:mo></mml:math>" @default.
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• W1976720753 doi "https://doi.org/10.1016/j.dam.2006.11.014" @default.
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