Stephens-Davidowitz
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Related Articles from SNS
Majorization and Gaussian-Mass Maximality for Construction-A Lattices from Binary Self-Dual Codes
arXiv:2606.03482v1 Announce Type: cross Abstract: Regev and Stephens-Davidowitz conjectured that the integer lattice maximizes Gaussian mass among integral lattices of a given rank. We prove this, including the equality case, for all unimodular Construction-A lattices arising from binary self-dual codes. The proof reduces the theta-series inequality to a sharp majorization statement for codes: if $C$ is a binary self-dual $[2k,k]$ code, then the half-weight distribution of $C$ is dominated...
Majorization and Gaussian-Mass Maximality for Construction-A Lattices from Binary Self-Dual Codes
Announce Type: replace-cross Abstract: Regev and Stephens-Davidowitz conjectured that the integer lattice maximizes Gaussian mass among integral lattices of a given rank. We prove this, including the equality case, for all unimodular Construction-A lattices arising from binary self-dual codes. The proof reduces the theta-series inequality to a sharp majorization statement for codes: if $C$ is a binary self-dual $[2k,k]$ code, then the half-weight distribution of $C$ is dominated in convex...