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A partition of the hypercube into maximally nonparallel Hamming codes

· 2012 · cs.IT · arXiv 1210.0010

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abstract

By using the Gold map, we construct a partition of the hypercube into cosets of Hamming codes such that for every two cosets the corresponding Hamming codes are maximally nonparallel, that is, their intersection cardinality is as small as possible to admit nonintersecting cosets.

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The Structure of Extremal Bad Science Matrices

math.FA · 2025-09-11 · conditional · novelty 7.0

For unit-row matrices, the maximal average sup-norm over Rademacher vectors is sqrt(2 log(2n)) - log log(2n)/(2 sqrt(2 log(2n))) + o(1/sqrt(log n)) for explicit Hadamard-based matrices and random sign matrices, with extremizers shown to induce nearly equal-volume, isoperimetrically optimal Voronoi…

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  • The Structure of Extremal Bad Science Matrices math.FA · 2025-09-11 · conditional · none · ref 9 · internal anchor

    For unit-row matrices, the maximal average sup-norm over Rademacher vectors is sqrt(2 log(2n)) - log log(2n)/(2 sqrt(2 log(2n))) + o(1/sqrt(log n)) for explicit Hadamard-based matrices and random sign matrices, with extremizers shown to induce nearly equal-volume, isoperimetrically optimal Voronoi…