Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ideal codes over separable ring extensions   This paper investigates the application of the theoretical algebraic notion
of a separable ring extension, in the realm of cyclic convolutional codes or,
more generally, ideal codes. We work under very mild conditions, that cover all
previously known as well as new non trivial examples. It is proved that ideal
codes are direct summands as left ideals of the underlying non-commutative
algebra, in analogy with cyclic block codes. This implies, in particular, that
they are generated by an idempotent element. Hence, by using a suitable
separability element, we design an efficient algorithm for computing one of
such idempotents.

26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc