Why it matters
Hadamard matrices connect combinatorial design, coding theory, signal processing, and extremal determinant problems.
Context and known approaches
Many infinite construction families and verified orders are known, but no construction covers every multiple of four.
Formal boundary
For every k∈N, there exists H∈{−1,1}^(4k×4k) with HHᵀ=4kI.
Known partial results
Pending review. No structured partial-result note has been added to this dossier.
Source trail
- Wikipedia — Definitions, constructions, and conjecture status.
- Wikipedia open-problems list — Composite index by mathematical field.