| 要約: | One of the fastest known general techniques for computing permanents is Ryser’s formula. On this note, we show that this formula over Sylvester Hadamard matrices of order <inline-formula><math display="inline"><semantics><msup><mn>2</mn><mi>m</mi></msup></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><msub><mi>H</mi><mi>m</mi></msub></semantics></math></inline-formula>, can be carried out by enumerating <i>m</i>-variable Boolean functions with an arbitrary Walsh spectrum. As a consequence, the quotient <inline-formula><math display="inline"><semantics><mrow><mi>p</mi><mi>e</mi><mi>r</mi><mrow><mo>(</mo><msub><mi>H</mi><mi>m</mi></msub><mo>)</mo></mrow><mo>/</mo><msup><mn>2</mn><msup><mn>2</mn><mi>m</mi></msup></msup></mrow></semantics></math></inline-formula> might be a measure of the “density” of <i>m</i>-variable Boolean functions with high nonlinearity.
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