Constanza Riera

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— Generalisations of the bent property of a Boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic Boolean functions are related to simple graphs and it is shown that the orbit generated by successive local complementations on a graph can be found within the transform spectra(More)
We relate the one-and two-variable interlace polynomials of a graph to the spectra of a quadratic boolean function with respect to a strategic subset of local unitary transforms. By so doing we establish links between graph theory, cryptography, coding theory, and quantum entanglement. We establish the form of the interlace polynomial for certain functions,(More)
In the first part of this paper [16], some results on how to compute the flat spectra of Boolean constructions w.r.t. n were presented, and the relevance of Local Complementation to the quadratic case was indicated. In this second part, the results are applied to develop recursive formulae for the numbers of flat spectra of some structural quadratics.(More)
We describe an operation to dynamically adapt the structure of the Tanner graph used during iterative decoding. Codes on graphs– most importantly, low-density parity-check (LDPC) codes–exploit ran-domness in the structure of the code. Our approach is to introduce a similar degree of controlled randomness into the operation of the message-passing decoder, to(More)
—This work is an extension of our previous work on an iterative soft decision decoder for high-density parity-check codes, using a graph-local operation known as edge-local complementation (ELC). The random application of ELC is replaced by ELC operations to target the inferred least reliable codeword positions, in between sum-product algorithm iterations.(More)
—In this paper, we propose to enhance the performance of the sum-product algorithm (SPA) by interleaving SPA iterations with a random local graph update rule. This rule is known as edge local complementation (ELC), and has the effect of modifying the Tanner graph while preserving the code. We have previously shown how the ELC operation can be used to(More)
The name 'graph state' is used to describe a certain class of pure quantum state which models a physical structure on which one can perform measurement-based quantum computing, and which has a natural graphical description. We present the two-graph state, this being a generalisation of the graph state and a two-graph representation of a stabilizer state.(More)
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 orbits of graphs and error-correcting codes. We define a new graph class, ELC-preserved graphs, comprising all graphs that have an ELC orbit of size one. Through an exhaustive(More)