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- W1566681845 abstract "We say that a binary linear code C has a geometric representation if there exists a two dimensional simplicial complex D such that C is a punctured code of the kernel ker D of the incidence matrix of D and dim C = dim ker D. We show that every binary linear code has a geometric representation that can be embedded into R^4. Moreover, we show that a binary linear code C has a geometric representation in R^3 if and only if there exists a graph G such that C equals the cut space of G. This is a polynomially testable property and hence we can conclude that there is a polynomial algorithm that decides the minimal dimension of a geometric representation of a binary linear code." @default.
- W1566681845 created "2016-06-24" @default.
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- W1566681845 date "2012-12-05" @default.
- W1566681845 modified "2023-09-27" @default.
- W1566681845 title "Geometric representations of binary codes embeddable in three dimensions" @default.
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