[Todos CMAT] Seminario de Álgebra del IMERL - Daniel Panario (Carleton University)

[seminarios en cmat.edu.uy]

Seminario de Álgebra del IMERL
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Título: "Finite Fields in Combinatorial Arrays: Constructions and Applications"

Expositor: Daniel Panario (Carleton University)

Resumen:
 
We discuss constructions based on finite fields of three types of
combinatorial arrays: orthogonal, covering and ordered orthogonal   arrays. In
this talk, for each of these arrays, we briefly explain   constructions based on
finite fields, and main applications.   Other combinatorial arrays have been
similarly considered in the   literature, including permutation arrays,
frequency permutation   arrays, hypercubes and Costas arrays, but we do not
cover here.    An Orthogonal Array (OA) of strength $t$ on $v$ symbols is an
array   with the property that, for every $t$-combination of column vectors,
every one of the possible $v^t$ $t$-tuples of symbols appears as a   row
``exactly'' once in the subarray defined by these column vectors.   OAs have
been applied in coding theory and in cryptography. They are   equivalent to MDS
(maximum distance separable) codes where the   strength of the OA is closely
related to the minimum distance of the   code. OAs are also closely related to
secret sharing in cryptography.   An Ordered Orthogonal Arrays (OOA) is a
generalization of OAs where   the coverage property applies to some selected
columns of the array.   Similarly, a Covering Array of strength $t$ on $v$
symbols is an array   with the property that, for every $t$-combination of
column vectors,   every one of the possible $v^t$ $t$-tuples of symbols appears
as a   row ``at least'' once in the subarray defined by these column vectors.
Covering arrays are used to reduce the number of tests in application   areas
such as software testing and group testing.    A common theme on several recent
constructions of these arrays is   the use of linear feedback shift register
(LFSR) sequences and finite   fields. Arrays whose rows are cyclic shifts of a
sequence over a   finite field possess many combinatorial properties. They have
been   used to build arrays attaining a high number of $t$-subsets of   columns
with the desired ``coverage property''. We provide examples   of applications of
these combinatorial arrays.
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Viernes 18/8 a las 11:15, Sala de Seminarios del IMERL y a través de Zoom

Contacto: Marco A. Pérez - mperez en fing.edu.uy
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Información     de     acceso a Zoom / Zoom access info:  Enlace / link:
https://salavirtual-udelar.zoom.us/j/85001311823   ID     de     reunión /
Meeting ID:  850 0131 1823   Nota importante: Después de la charla, tomaremos un
refrigerio en la Sala de Vida del IMERL, alrededor de las 12:30, con motivo del
inicio del ciclo de charlas de este semestre. Están cordialmente invitados. :)
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