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dc.contributor.authorCascudo, Ignacio
dc.contributor.authorGundersen, Jaron Skovsted
dc.contributor.authorRuano Benito, Diego 
dc.date.accessioned2020-01-14T11:02:19Z
dc.date.available2020-01-14T11:02:19Z
dc.date.issued2020
dc.identifier.citationI. Cascudo, J.S. Gundersen, D. Ruano: Squares of Matrix-product Codes. Finite Fields and their Applications. Volume 62, 101606 (2020)es
dc.identifier.issn1071-5797es
dc.identifier.urihttp://uvadoc.uva.es/handle/10324/40143
dc.description.abstractThe component-wise or Schur product $C*C'$ of two linear error-correcting codes $C$ and $C'$ over certain finite field is the linear code spanned by all component-wise products of a codeword in $C$ with a codeword in $C'$. When $C=C'$, we call the product the square of $C$ and denote it $C^{*2}$. Motivated by several applications of squares of linear codes in the area of cryptography, in this paper we study squares of so-called matrix-product codes, a general construction that allows to obtain new longer codes from several ``constituent'' codes. We show that in many cases we can relate the square of a matrix-product code to the squares and products of their constituent codes, which allow us to give bounds or even determine its minimum distance. We consider the well-known $(u,u+v)$-construction, or Plotkin sum (which is a special case of a matrix-product code) and determine which parameters we can obtain when the constituent codes are certain cyclic codes. In addition, we use the same techniques to study the squares of other matrix-product codes, for example when the defining matrix is Vandermonde (where the minimum distance is in a certain sense maximal with respect to matrix-product codes).es
dc.format.mimetypeapplication/pdfes
dc.language.isoenges
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.titleSquares of matrix-product codeses
dc.typeinfo:eu-repo/semantics/articlees
dc.identifier.doi10.1016/j.ffa.2019.101606es
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S1071579719301091?via%3Dihubes
dc.identifier.publicationfirstpage101606es
dc.identifier.publicationtitleFinite Fields and Their Applicationses
dc.identifier.publicationvolume62es
dc.peerreviewedSIes
dc.description.projectThis work is supported by the Danish Council for IndependentResearch: grant DFF-4002-00367, theSpanish Ministry of Economy/FEDER: grant RYC-2016-20208 (AEI/FSE/UE), the Spanish Ministry of Science/FEDER: grant PGC2018-096446-B-C21, and Junta de CyL (Spain): grant VA166G1es
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.type.hasVersioninfo:eu-repo/semantics/draftes


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