Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of MDS Euclidean Self-Dual Codes via Two Subsets   The parameters of a $q$-ary MDS Euclidean self-dual codes are completely
determined by its length and the construction of MDS Euclidean self-dual codes
with new length has been widely investigated in recent years. In this paper, we
give a further study on the construction of MDS Euclidean self-dual codes via
generalized Reed-Solomon (GRS) codes and their extended codes. The main idea of
our construction is to choose suitable evaluation points such that the
corresponding (extended) GRS codes are Euclidean self-dual.
  Firstly, we consider the evaluation set consists of two disjoint subsets, one
of which is based on the trace function, the other one is a union of a subspace
and its cosets. Then four new families of MDS Euclidean self-dual codes are
constructed. Secondly, we give a simple but useful lemma to ensure that the
symmetric difference of two intersecting subsets of finite fields can be taken
as the desired evaluation set. Based on this lemma, we generalize our first
construction and provide two new families of MDS Euclidean self-dual codes.
Finally, by using two multiplicative subgroups and their cosets which have
nonempty intersection, we present three generic constructions of MDS Euclidean
self-dual codes with flexible parameters. Several new families of MDS Euclidean
self-dual codes are explicitly constructed.

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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th