Infinite families of t-designs from the binomial $$x^{4}+x^{3}$$ over $$\mathrm {GF}(2^n)$$
| Autor: | Can Xiang, Xin Ling |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Algebra and Number Theory
Binomial (polynomial) Applied Mathematics Image (category theory) 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology Quadratic function 01 natural sciences GF(2) Combinatorics X.3 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering Mathematics |
| Zdroj: | Applicable Algebra in Engineering, Communication and Computing. 34:411-421 |
| ISSN: | 1432-0622 0938-1279 |
| DOI: | 10.1007/s00200-021-00512-9 |
| Popis: | Combinatorial t-designs have nice applications in coding theory, finite geometries and engineering areas. t-designs can be constructed from image sets of a fixed size of some special polynomials. This paper constructs t-designs from the quadratic polynomial $$x^{4}+x^{3}$$ over $$\mathrm {GF}(2^{n})$$ and determine their parameters. We yield 2- $$\left( 2^n,3\cdot 2^{n-2},3\cdot 2^{n-2}\left( 3\cdot 2^{n-2}-1 \right) \right) $$ designs for n even and 3- $$\left( 2^n,2^{n-1},2^{n-1}\left( 2^{n-2}-1 \right) \right) $$ designs for n odd. |
| Databáze: | OpenAIRE |
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