On Lengths of \(\mathbb{F}_2[x,y,z]/(x^{d_1}, y^{d_2},z^{d_3}, x+y+z)\)

On Lengths of \(\mathbb{F}_2[x,y,z]/(x^{d_1}, y^{d_2},z^{d_3}, x+y+z)\)

In this paper, we provide a formula for the vector space dimension of the ring \(\mathbb{F}_2[x,y,z]/(x^{d_1}, y^{d_2},z^{d_3}, x+y+z)\) over \(\mathbb{F}_2\) when \(d_1,d_2,d_3\) all lie between successive powers of \(2\). For general \(d_1,d_2,d_3\), we provide a simple algorithm to calculate the...

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Veröffentlicht in:arXiv.org 2024-08
Hauptverfasser: Han, Fiona, Kenkel, Jennifer, Li, Daniel, Venkatesh, Sridhar, Wiles, Ashley
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Cryptography
Field theory
Mathematical analysis
Polynomials
Questions
Quotients
Rings (mathematics)
Vector spaces
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Zusammenfassung:In this paper, we provide a formula for the vector space dimension of the ring \(\mathbb{F}_2[x,y,z]/(x^{d_1}, y^{d_2},z^{d_3}, x+y+z)\) over \(\mathbb{F}_2\) when \(d_1,d_2,d_3\) all lie between successive powers of \(2\). For general \(d_1,d_2,d_3\), we provide a simple algorithm to calculate the vector space dimension of \(\mathbb{F}_2[x,y,z]/(x^{d_1}, y^{d_2},z^{d_3}, x+y+z)\) by combining our formula with certain results of Chungsim Han (1992).
ISSN:2331-8422