Infinite families of \(t\)-designs from the binomial \(x^4 +x^3\) over \(\mathrm{GF}(2^n)\)

DOI10.1007/s00200-021-00512-9zbMath1522.05016OpenAlexW3160419478MaRDI QIDQ6157857

Xin Ling, Can Xiang

Publication date: 12 May 2023

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00200-021-00512-9

zbMATH Keywords

projective plane\(t\)-designalgebraic curvespolynomialfinite filed

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Blocking sets, ovals, (k)-arcs (51E21) Special polynomials in general fields (12E10)

Cites Work

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• On \(x^{q+1}+ax+b\)
• Designs in additive codes over GF(4)
• A coding theoretic approach to extending designs
• Steiner systems \(S(2,4,v)\) -- a survey
• Infinite families of 2-designs and 3-designs from linear codes
• Combinatorial \(t\)-designs from special functions
• Combinatorial \(t\)-designs from quadratic functions
• Steiner systems \(S(2, 4, \frac{3^m-1}{2})\) and 2-designs from ternary linear codes of length \(\frac{3^m-1}{2}\)
• Infinite families of 3-designs from a type of five-weight code
• Linear Codes From Some 2-Designs
• Codes, Differentially $\delta$ -Uniform Functions, and $t$ -Designs
• Infinite families of 3‐designs from APN functions

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