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- W4386838313 abstract "Abstract In this paper, we consider the affine variety codes obtained evaluating the polynomials $$by=a_kx^k+ldots +a_1x+a_0$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>b</mml:mi> <mml:mi>y</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:msup> <mml:mi>x</mml:mi> <mml:mi>k</mml:mi> </mml:msup> <mml:mo>+</mml:mo> <mml:mo>…</mml:mo> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mi>x</mml:mi> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> , $$b,a_iin {mathbb {F}}_{q^r}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>b</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>a</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:mo>∈</mml:mo> <mml:msub> <mml:mi>F</mml:mi> <mml:msup> <mml:mi>q</mml:mi> <mml:mi>r</mml:mi> </mml:msup> </mml:msub> </mml:mrow> </mml:math> , at the affine $${{mathbb {F}}}_{q^r}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>F</mml:mi> <mml:msup> <mml:mi>q</mml:mi> <mml:mi>r</mml:mi> </mml:msup> </mml:msub> </mml:math> -rational points of the Norm-Trace curve. In particular, we investigate the weight distribution and the set of minimal codewords. Our approach, which uses tools of algebraic geometry, is based on the study of the absolute irreducibility of certain algebraic varieties." @default.
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- W4386838313 date "2023-09-18" @default.
- W4386838313 modified "2023-10-06" @default.
- W4386838313 title "Minimal codewords in Norm-Trace codes" @default.
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- W4386838313 doi "https://doi.org/10.1007/s00010-023-00985-8" @default.
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