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On sequency-complete and sequency-ordered matrices

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arxiv 2402.11003 v1 pith:LTBYVYE2 submitted 2024-02-16 math.CO

classification math.CO
keywords matricessequency-completesequency-orderedarbitraryconceptresultssequencysizes
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The concept of sequency holds a fundamental significance in signal analysis using Walsh basis functions. In this study, we closely examine the concept of sequency and explore the properties of sequency-complete and sequency-ordered matrices. We obtain results on cardinalities of sets containing sequency-complete and sequency-ordered matrices of arbitrary sizes. We present methods for obtaining interesting classes of sequency-complete and sequency-ordered matrices of arbitrary sizes. We also provide results on the sequencies of columns in tensor products involving two or more matrices.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantum algorithm for edge detection in digital grayscale images

    quant-ph 2025-07 conditional novelty 5.0 of 10

    A quantum edge detection algorithm based on the sequency-ordered Walsh-Hadamard transform and a quantum high-pass filter achieves O(log N) circuit depth when state preparation is excluded.

  2. Generalized tensor transforms and their applications in classical and quantum computing

    quant-ph 2025-07 reject novelty 3.0 of 10

    The claim that tunable tensor-product transforms outperform fixed transforms for quantum compression and encoding rests on fits to the data, not on independent predictions.

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