The orthogonal projector reduction from PEP for LCD codes to GI closes under bilinear forms M = aI + bJ, with codes reducible precisely when hull dimension is at most 1 under an explicit hull-vector condition.
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The Closure of LCD-to-GI Reductions via Generalized Inner Products
The orthogonal projector reduction from PEP for LCD codes to GI closes under bilinear forms M = aI + bJ, with codes reducible precisely when hull dimension is at most 1 under an explicit hull-vector condition.