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Spectrally Bounded Sequences, Codes, and States: Graph Constructions and Entanglement

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Book cover Cryptography and Coding (Cryptography and Coding 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2260))

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Abstract

A recursive construction is provided for sequence sets which possess good Hamming Distance and low Peak-to-Average Power Ratio (PAR) under any Local Unitary Unimodular Transform. We identify a subset of these sequences that map to binary indicators for linear and nonlinear Factor Graphs, after application of subspace Walsh-Hadamard Transforms. Finally we investigate the quantum PARl measure of ‘Linear Entanglement’ (LE) under any Local Unitary Transform, where optimum LE implies optimum weight hierarchy of an associated linear code.

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Author information

Authors and Affiliations

  1. Code Theory Group, Inst. for Informatikk, HIB, University of Bergen, Norway

    Matthew G. Parker

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  1. Matthew G. Parker
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Editor information

Editors and Affiliations

  1. Faculty of Applied Sciences, Department of Communication Systems, Lancaster University, LA1 4YR, Lancaster, UK

    Bahram Honary

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© 2001 Springer-Verlag Berlin Heidelberg

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Parker, M.G. (2001). Spectrally Bounded Sequences, Codes, and States: Graph Constructions and Entanglement. In: Honary, B. (eds) Cryptography and Coding. Cryptography and Coding 2001. Lecture Notes in Computer Science, vol 2260. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45325-3_30

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  • DOI: https://doi.org/10.1007/3-540-45325-3_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43026-1

  • Online ISBN: 978-3-540-45325-3

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