Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Binary self-dual codes of various lengths with new weight enumerators
  from a modified bordered construction and neighbours   In this work, we define a modification of a bordered construction for
self-dual codes which utilises $\lambda$-circulant matrices. We provide the
necessary conditions for the construction to produce self-dual codes over
finite commutative Frobenius rings of characteristic 2. Using the modified
construction together with the neighbour construction, we construct many binary
self-dual codes of lengths 54, 68, 82 and 94 with weight enumerators that have
previously not been known to exist.

5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin