Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the nonexistence of $[\binom{2m}{m-1}, 2m, \binom{2m-1}{m-1}]$, $m$
  odd, complex orthogonal design   Complex orthogonal designs (CODs) are used to construct space-time block
codes. COD $\mathcal{O}_z$ with parameter $[p, n, k]$ is a $p\times n$ matrix,
where nonzero entries are filled by $\pm z_i$ or $\pm z^*_i$, $i = 1, 2,...,
k$, such that $\mathcal{O}^H_z \mathcal{O}_z =
(|z_1|^2+|z_2|^2+...+|z_k|^2)I_{n \times n}$. Adams et al. in "The final case
of the decoding delay problem for maximum rate complex orthogonal designs,"
IEEE Trans. Inf. Theory, vol. 56, no. 1, pp. 103-122, Jan. 2010, first proved
the nonexistence of $[\binom{2m}{m-1}, 2m, \binom{2m-1}{m-1}]$, $m$ odd, COD.
Combining with the previous result that decoding delay should be an integer
multiple of $\binom{2m}{m-1}$, they solved the final case $n \equiv 2 \pmod 4$
of the decoding delay problem for maximum rate complex orthogonal designs.
  In this paper, we give another proof of the nonexistence of COD with
parameter $[\binom{2m}{m-1}, 2m, \binom{2m-1}{m-1}]$, $m$ odd. Our new proof is
based on the uniqueness of $[\binom{2m}{m-1}, 2m-1, \binom{2m-1}{m-1}]$ under
equivalence operation, where an explicit-form representation is proposed to
help the proof. Then, by proving it's impossible to add an extra orthogonal
column on COD $[\binom{2m}{m-1}, 2m-1, \binom{2m-1}{m-1}]$ when $m$ is odd, we
complete the proof of the nonexistence of COD $[\binom{2m}{m-1}, 2m,
\binom{2m-1}{m-1}]$.

13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th