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The aim is to understand when canonical codes associated with classical groups are self-orthogonal over finite fields.

July 14, 2026Open Access

Classical-Group Q-Scope and the Canonicalization–Isometry Principle

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The aim is to understand when canonical codes associated with classical groups are self-orthogonal over finite fields.
Analyzed the conditions for self-orthogonality on canonical codes derived from various classical groups.
Established a dichotomy based on the scale factor normalization for different families of groups.
Utilized invariant-form lemma and Schubert-cell argument for thorough field analysis.
Canonical codes of PSL, PΩ⁺, PΩ⁻, and Sp are self-orthogonal if and only if q ∈ {2, 3}.
Canonical codes of PSU are self-orthogonal exclusively when q = 2, with low-dimensional exceptions.
Generalization of the classical Gleason–Pierce–Ward theorem to a broader self-orthogonal coding framework.

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Randomized trial reveals self-orthogonality in classical groups, indicating a universal geometric property.

Vladimer Merebashvili (2026) studied this question.

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