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<h2 style="font-size:1.2em;">Seminario de Álgebra del IMERL</h2>
<h3 style="font-size:1em;">Título: <em>Finite Fields in Combinatorial Arrays: Constructions and Applications</em></h3>
<h3 style="font-size:1em;">Expositor: Daniel Panario <span style="font-weight:400;">(Carleton University)</span></h3>
<div style="font-size:1em!important;"><p><b>Resumen: </b><span>We discuss constructions based on finite fields of three types of </span><span>combinatorial arrays: orthogonal, covering and ordered orthogonal </span><span>arrays. In this talk, for each of these arrays, we briefly explain </span><span>constructions based on finite fields, and main applications. </span><span>Other combinatorial arrays have been similarly considered in the </span><span>literature, including permutation arrays, frequency permutation </span><span>arrays, hypercubes and Costas arrays, but we do not cover here.</span><br/><br/><span>An Orthogonal Array (OA) of strength $t$ on $v$ symbols is an array </span><span>with the property that, for every $t$-combination of column vectors, </span><span>every one of the possible $v^t$ $t$-tuples of symbols appears as a </span><span>row ``exactly'' once in the subarray defined by these column vectors. </span><span>OAs have been applied in coding theory and in cryptography. They are </span><span>equivalent to MDS (maximum distance separable) codes where the </span><span>strength of the OA is closely related to the minimum distance of the </span><span>code. OAs are also closely related to secret sharing in cryptography. </span><span>An Ordered Orthogonal Arrays (OOA) is a generalization of OAs where </span><span>the coverage property applies to some selected columns of the array. </span><span>Similarly, a Covering Array of strength $t$ on $v$ symbols is an array </span><span>with the property that, for every $t$-combination of column vectors, </span><span>every one of the possible $v^t$ $t$-tuples of symbols appears as a </span><span>row ``at least'' once in the subarray defined by these column vectors. </span><span>Covering arrays are used to reduce the number of tests in application </span><span>areas such as software testing and group testing.</span><br/><br/><span>A common theme on several recent constructions of these arrays is </span><span>the use of linear feedback shift register (LFSR) sequences and finite </span><span>fields. Arrays whose rows are cyclic shifts of a sequence over a </span><span>finite field possess many combinatorial properties. They have been </span><span>used to build arrays attaining a high number of $t$-subsets of </span><span>columns with the desired ``coverage property''. We provide examples </span><span>of applications of these combinatorial arrays.</span></p></div>
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<p style="font-size:1em;"><b>Viernes 18/8 a las 11:15</b><br>
<b>Sala de Seminarios del IMERL y a través de Zoom</b>
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<p style="font-size:1em;"><b>Contacto: </b>Marco A. Pérez - <a href="mailto:mperez@fing.edu.uy">mperez@fing.edu.uy</a></p>
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<p><strong>Información<span> </span><span><span class="il">de</span></span><span> </span>acceso a Zoom / Zoom access info:</strong><br/><br/><strong>Enlace / link:</strong><span> </span><a href="https://salavirtual-udelar.zoom.us/j/85001311823" target="_blank" rel="noopener">https://salavirtual-udelar.zoom.us/j/85001311823</a><br/><br/><strong>ID<span> </span><span><span class="il">de</span></span><span> </span>reunión / Meeting ID:</strong><span> 850 0131 1823</span><br/><br/><strong>Nota importante: </strong>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. :)</p><hr>
Más seminarios en: <a href="http://www.cmat.edu.uy/seminarios">http://www.cmat.edu.uy/seminarios</a>
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