Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Codebooks from generalized bent $\mathbb{Z}_4$-valued quadratic forms   Codebooks with small inner-product correlation have application in unitary
space-time modulations, multiple description coding over erasure channels,
direct spread code division multiple access communications, compressed sensing,
and coding theory. It is interesting to construct codebooks (asymptotically)
achieving the Welch bound or the Levenshtein bound. This paper presented a
class of generalized bent $\mathbb{Z}_4$-valued quadratic forms, which contain
functions of Heng and Yue (Optimal codebooks achieving the Levenshtein bound
from generalized bent functions over $\mathbb{Z}_4$. Cryptogr. Commun. 9(1),
41-53, 2017). By using these generalized bent $\mathbb{Z}_4$-valued quadratic
forms, we constructs optimal codebooks achieving the Levenshtein bound. These
codebooks have parameters $(2^{2m}+2^m,2^m)$ and alphabet size $6$.

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The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci