Infinite families of $2$-designs from two classes of linear codes

Chunming Tang; Qi Wang; Rong Wang; Xiaoni Du

arxiv: 1903.07459 · v1 · pith:37PTEKPRnew · submitted 2019-03-18 · 🧮 math.CO

Infinite families of 2-designs from two classes of linear codes

Xiaoni Du , Rong Wang , Chunming Tang , Qi Wang This is my paper

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keywords codesdesignsweightclassescodewordsfamiliesfixedinfinite

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The interplay between coding theory and $t$-designs has attracted a lot of attention for both directions. It is well known that the supports of all codewords with a fixed weight in a code may hold a $t$-design. In this paper, by determining the weight distributions of two classes of linear codes, we derive infinite families of $2$-designs from the supports of codewords with a fixed weight in these codes, and explicitly obtain their parameters.

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Combinatorial t-designs from quadratic functions
cs.IT 2019-07 unverdicted novelty 6.0

Quadratic functions over finite fields produce infinite families of 2-designs with explicitly determined parameters, generalizing prior examples and confirming a 2019 conjecture.