What does this research mean for the field?

The [[13,7,3]]_3 ternary CSS quantum stabilizer code and its dimension-indexed family, derived from the Topological Vortex Logic framework, possess distinct algebraic and geometric structures, including closed-form weight enumerators, specific low-weight normalizer species, and equivariant Witt decompositions. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research aims to investigate the algebraic and geometric structure of the [[13,7,3]]₃ quantum stabilizer code within the Topological Vortex Logic framework.

August 2, 2026Open Access

Quantum Error-Correcting Structure of Topological Vortex Logic: The [[13,7,3]]_3 CSS Family and its Algebraic Geometry

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This research aims to investigate the algebraic and geometric structure of the [[13,7,3]]₃ quantum stabilizer code within the Topological Vortex Logic framework.
Establishment of the structure of the [[13,7,3]]₃ code and its dimension-indexed family.
Application of projective geometry principles to derive the parity-check matrix; analysis of structural properties.
Development of low-weight normalizer species and equivariant Witt decomposition over F₃.
The [[13,7,3]]₃ code exhibits distinct behavioral characteristics, such as positive logical dimension and unique physical length.
The symplectic-weight distribution leads to refined classifications of low-weight logical operators.
Maximal-Witt-index results reinforce the framework of ternary projective Hamming families.

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Implication

Randomized trial explores quantum error correction in ternary codes, indicating applications in quantum computing.

Cite This Study

Vladimer Merebashvili (2026) studied this question.

synapsesocial.com/papers/6a6eeadb1b0468a7eeab3704 https://doi.org/10.5281/zenodo.21705393

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Quantum Error-Correcting Structure of Topological Vortex Logic: The [[13,7,3]]_3 CSS Family and its Algebraic Geometry

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Implication

Cite This Study

Quantum Error-Correcting Structure of Topological Vortex Logic: The [[13,7,3]]_3 CSS Family and its Algebraic Geometry

Key Points

Discussion

Implication

Cite This Study

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