A graphical representation of binary linear codes

05/21/2022

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by   Lisbeth Danyeli Delgado Ordoñez, et al.

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A binary [n,k]-linear code 𝒞 is a k-dimensional subspace of 𝔽_2^n. For x∈𝔽_2^n, the set x+𝒞 is a coset of 𝒞. In this work we study a partial ordering on the set of cosets of a binary linear code 𝒞 of length n and we construct a graph using the orphan structure of this code.