Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new method for constructing linear codes with small hulls   The hull of a linear code over finite fields is the intersection of the code
and its dual, which was introduced by Assmus and Key. In this paper, we develop
a method to construct linear codes with trivial hull ( LCD codes) and
one-dimensional hull by employing the positive characteristic analogues of
Gauss sums. These codes are quasi-abelian, and sometimes doubly circulant. Some
sufficient conditions for a linear code to be an LCD code (resp. a linear code
with one-dimensional hull) are presented. It is worth mentioning that we
present a lower bound on the minimum distances of the constructed linear codes.
As an application, using these conditions, we obtain some optimal or almost
optimal LCD codes (resp. linear codes with one-dimensional hull) with respect
to the online Database of Grassl.

10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
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The categories of this paper are: eess
26
The categories of this paper are: bayes-an
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The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
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The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat