Matches in SemOpenAlex for { <https://semopenalex.org/work/W1647275948> ?p ?o ?g. }
Showing items 1 to 79 of
79
with 100 items per page.
- W1647275948 abstract "Toric codes are a class of $m$-dimensional cyclic codes introduced recently by J. Hansen. They may be defined as evaluation codes obtained from monomials corresponding to integer lattice points in an integral convex polytope $P subseteq R^m$. As such, they are in a sense a natural extension of Reed-Solomon codes. Several authors have used intersection theory on toric surfaces to derive bounds on the minimum distance of some toric codes with $m = 2$. In this paper, we will provide a more elementary approach that applies equally well to many toric codes for all $m ge 2$. Our methods are based on a sort of multivariate generalization of Vandermonde determinants that has also been used in the study of multivariate polynomial interpolation. We use these Vandermonde determinants to determine the minimum distance of toric codes from rectangular polytopes and simplices. We also prove a general result showing that if there is a unimodular integer affine transformation taking one polytope $P_1$ to a second polytope $P_2$, then the corresponding toric codes are monomially equivalent (hence have the same parameters). We use this to begin a classification of two-dimensional toric codes with small dimension." @default.
- W1647275948 created "2016-06-24" @default.
- W1647275948 creator A5050473614 @default.
- W1647275948 creator A5083027824 @default.
- W1647275948 date "2005-06-29" @default.
- W1647275948 modified "2023-09-27" @default.
- W1647275948 title "On $m$-dimensional toric codes" @default.
- W1647275948 cites W1499738674 @default.
- W1647275948 cites W1597196612 @default.
- W1647275948 cites W2027983424 @default.
- W1647275948 cites W21535682 @default.
- W1647275948 cites W2180062674 @default.
- W1647275948 cites W2264065105 @default.
- W1647275948 cites W2953376425 @default.
- W1647275948 hasPublicationYear "2005" @default.
- W1647275948 type Work @default.
- W1647275948 sameAs 1647275948 @default.
- W1647275948 citedByCount "6" @default.
- W1647275948 countsByYear W16472759482020 @default.
- W1647275948 crossrefType "posted-content" @default.
- W1647275948 hasAuthorship W1647275948A5050473614 @default.
- W1647275948 hasAuthorship W1647275948A5083027824 @default.
- W1647275948 hasConcept C114614502 @default.
- W1647275948 hasConcept C118615104 @default.
- W1647275948 hasConcept C121332964 @default.
- W1647275948 hasConcept C145691206 @default.
- W1647275948 hasConcept C158693339 @default.
- W1647275948 hasConcept C199360897 @default.
- W1647275948 hasConcept C201958917 @default.
- W1647275948 hasConcept C202444582 @default.
- W1647275948 hasConcept C33923547 @default.
- W1647275948 hasConcept C41008148 @default.
- W1647275948 hasConcept C5052557 @default.
- W1647275948 hasConcept C55294529 @default.
- W1647275948 hasConcept C62520636 @default.
- W1647275948 hasConcept C92757383 @default.
- W1647275948 hasConcept C97137487 @default.
- W1647275948 hasConceptScore W1647275948C114614502 @default.
- W1647275948 hasConceptScore W1647275948C118615104 @default.
- W1647275948 hasConceptScore W1647275948C121332964 @default.
- W1647275948 hasConceptScore W1647275948C145691206 @default.
- W1647275948 hasConceptScore W1647275948C158693339 @default.
- W1647275948 hasConceptScore W1647275948C199360897 @default.
- W1647275948 hasConceptScore W1647275948C201958917 @default.
- W1647275948 hasConceptScore W1647275948C202444582 @default.
- W1647275948 hasConceptScore W1647275948C33923547 @default.
- W1647275948 hasConceptScore W1647275948C41008148 @default.
- W1647275948 hasConceptScore W1647275948C5052557 @default.
- W1647275948 hasConceptScore W1647275948C55294529 @default.
- W1647275948 hasConceptScore W1647275948C62520636 @default.
- W1647275948 hasConceptScore W1647275948C92757383 @default.
- W1647275948 hasConceptScore W1647275948C97137487 @default.
- W1647275948 hasLocation W16472759481 @default.
- W1647275948 hasOpenAccess W1647275948 @default.
- W1647275948 hasPrimaryLocation W16472759481 @default.
- W1647275948 hasRelatedWork W1668932619 @default.
- W1647275948 hasRelatedWork W1680342726 @default.
- W1647275948 hasRelatedWork W1984753322 @default.
- W1647275948 hasRelatedWork W1999113954 @default.
- W1647275948 hasRelatedWork W2007196505 @default.
- W1647275948 hasRelatedWork W2011223175 @default.
- W1647275948 hasRelatedWork W2027983424 @default.
- W1647275948 hasRelatedWork W2056558741 @default.
- W1647275948 hasRelatedWork W2059701611 @default.
- W1647275948 hasRelatedWork W2106703368 @default.
- W1647275948 hasRelatedWork W2593889002 @default.
- W1647275948 hasRelatedWork W2953376425 @default.
- W1647275948 hasRelatedWork W2963278054 @default.
- W1647275948 hasRelatedWork W3012586171 @default.
- W1647275948 hasRelatedWork W3042074279 @default.
- W1647275948 hasRelatedWork W3102274963 @default.
- W1647275948 hasRelatedWork W3103060901 @default.
- W1647275948 hasRelatedWork W3105909643 @default.
- W1647275948 hasRelatedWork W3135812225 @default.
- W1647275948 hasRelatedWork W594028326 @default.
- W1647275948 isParatext "false" @default.
- W1647275948 isRetracted "false" @default.
- W1647275948 magId "1647275948" @default.
- W1647275948 workType "article" @default.