87 citations · 388 across the 15 of their papers we have counts for
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On the classification of Hermitian self-dual additive codes over GF(9)
Lars Eirik Danielsen
Additive codes over GF(9) that are self-dual with respect to the Hermitian trace inner product have a natural application in quantum information theory, where they correspond to te…
On Graphs and Codes Preserved by Edge Local Complementation
Lars Eirik Danielsen, Matthew G. Parker, Constanza Riera +1
Orbits of graphs under local complementation (LC) and edge local complementation (ELC) have been studied in several different contexts. For instance, there are connections between…
Directed Graph Representation of Half-Rate Additive Codes over GF(4)
Lars Eirik Danielsen, Matthew G. Parker
We show that (n,2^n) additive codes over GF(4) can be represented as directed graphs. This generalizes earlier results on self-dual additive codes over GF(4), which correspond to u…
Interlace Polynomials: Enumeration, Unimodality, and Connections to Codes
Lars Eirik Danielsen, Matthew G. Parker
The interlace polynomial q was introduced by Arratia, Bollobas, and Sorkin. It encodes many properties of the orbit of a graph under edge local complementation (ELC). The interlace…
Edge Local Complementation and Equivalence of Binary Linear Codes
Lars Eirik Danielsen, Matthew G. Parker
Orbits of graphs under the operation edge local complementation (ELC) are defined. We show that the ELC orbit of a bipartite graph corresponds to the equivalence class of a binary…
On Pivot Orbits of Boolean Functions
Constanza Riera, Lars Eirik Danielsen, Matthew G. Parker
We derive a spectral interpretation of the pivot operation on a graph and generalise this operation to hypergraphs. We establish lower bounds on the number of flat spectra of a Boo…
On the Classification of All Self-Dual Additive Codes over GF(4) of Length up to 12
Lars Eirik Danielsen, Matthew G. Parker
We consider additive codes over GF(4) that are self-dual with respect to the Hermitian trace inner product. Such codes have a well-known interpretation as quantum codes and corresp…