4,441 research outputs found
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
Towers of Function Fields over Non-prime Finite Fields
Over all non-prime finite fields, we construct some recursive towers of
function fields with many rational places. Thus we obtain a substantial
improvement on all known lower bounds for Ihara's quantity , for with prime and odd. We relate the explicit equations to
Drinfeld modular varieties
Sums of units in function fields II - The extension problem
In 2007, Jarden and Narkiewicz raised the following question: Is it true that
each algebraic number field has a finite extension L such that the ring of
integers of L is generated by its units (as a ring)? In this article, we answer
the analogous question in the function field case.
More precisely, it is shown that for every finite non-empty set S of places
of an algebraic function field F | K over a perfect field K, there exists a
finite extension F' | F, such that the integral closure of the ring of
S-integers of F in F' is generated by its units (as a ring).Comment: 12 page
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