Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric representations of linear codes   We say that a linear code C over a field F is triangular representable if
there exists a two dimensional simplicial complex $\Delta$ such that C is a
punctured code of the kernel ker $\Delta$ of the incidence matrix of $\Delta$
over F and there is a linear mapping between C and ker $\Delta$ which is a
bijection and maps minimal codewords to minimal codewords. We show that the
linear codes over rationals and over GF(p), where p is a prime, are triangular
representable. In the case of finite fields, we show that this representation
determines the weight enumerator of C. We present one application of this
result to the partition function of the Potts model.
  On the other hand, we show that there exist linear codes over any field
different from rationals and GF(p), p prime, that are not triangular
representable. We show that every construction of triangular representation
fails on a very weak condition that a linear code and its triangular
representation have to have the same dimension.

10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th