Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An infinite family of antiprimitive cyclic codes supporting Steiner
  systems $S(3,8, 7^m+1)$   Coding theory and combinatorial $t$-designs have close connections and
interesting interplay. One of the major approaches to the construction of
combinatorial t-designs is the employment of error-correcting codes. As we all
known, some $t$-designs have been constructed with this approach by using
certain linear codes in recent years. However, only a few infinite families of
cyclic codes holding an infinite family of $3$-designs are reported in the
literature. The objective of this paper is to study an infinite family of
cyclic codes and determine their parameters. By the parameters of these codes
and their dual, some infinite family of $3$-designs are presented and their
parameters are also explicitly determined. In particular, the complements of
the supports of the minimum weight codewords in the studied cyclic code form a
Steiner system. Furthermore, we show that the infinite family of cyclic codes
admit $3$-transitive automorphism groups.

27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con