REVIEW 2 major objections 2 minor
This survey maps the code equivalence problem across formulations, algorithms, attacks, parameter regimes, and open hardness questions.
Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →
T0 review · grok-4.5
2026-07-15 02:42 UTC pith:7SIOOOG5
load-bearing objection Abstract-only survey of code equivalence: useful map if the full text delivers, but we cannot yet judge completeness or balance. the 2 major comments →
A Survey on Code Equivalence: The State-of-the-Art and Open Questions
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
By relating formulations of code equivalence, the algorithmic techniques used against them, the hardness assumptions that support them, and the known attacks with their effective parameter regimes and limits, the authors claim one can clarify the present hardness landscape and isolate the open questions that still matter.
What carries the argument
The code equivalence problem itself (deciding whether two linear codes differ only by a coordinate permutation, or by a more general isometry) together with its standard variants. This family of decision problems is the central object that organizes the survey’s comparisons of algorithms, hardness assumptions, and attack regimes.
Load-bearing premise
That the authors’ selection and organization of prior results, attacks, and parameter regimes is complete and balanced enough to serve as a reliable map of the field.
What would settle it
Exhibit a standard formulation, algorithm, or attack regime that is established in the literature yet is omitted or materially mischaracterized in the survey’s map of results and parameter ranges.
If this is right
- Cryptographic parameters that rest on code equivalence can be chosen with an explicit view of which attack regimes already apply.
- Hardness transfers between related formulations become easier to state once the relationships are laid out in one place.
- The listed open problems supply concrete next targets for reductions or algorithms in regimes that remain unsettled.
- Documented limits of known attacks mark where security arguments based on code equivalence are still plausible.
Where Pith is reading between the lines
- If the map is accurate, code-based schemes that reduce security to a code-equivalence variant can inherit clearer margins once the effective attack regimes are fixed.
- Closing the open formulation gaps the survey flags could produce new hardness reductions usable outside pure coding theory.
- A practical follow-on would be tabulated complexity estimates for the concrete parameter ranges used in current proposals.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript is a survey of the code equivalence problem and its variants. From the abstract, it claims to explain existing results while highlighting relationships among problem formulations, algorithmic techniques, and hardness assumptions; to systematically review known attacks together with the parameter regimes in which they are effective and their limitations; and to outline open problems and research directions intended to clarify the hardness landscape of code equivalence.
Significance. If the survey is complete, balanced, and accurate, it would be a useful reference for the coding-theory and post-quantum cryptography communities. A single map that relates formulations, algorithms, hardness assumptions, attack regimes, and open questions would help standardize comparisons and guide parameter selection and future hardness work. Because only the abstract is available, these strengths remain aspirational; the significance assessment is therefore conditional on the body delivering the claimed coverage without major omissions or mischaracterizations.
major comments (2)
- Only the abstract is available for review. The central claim of comprehensive, balanced coverage of formulations, algorithms, hardness assumptions, attacks (with effective parameter regimes and limitations), and open problems cannot be verified. Without the taxonomy, attack tables, regime statements, or open-problem arguments, it is impossible to assess whether the survey is load-bearing as a reliable map of the field. A full-text review is required before any accept/reject decision can be made on the manuscript's substance.
- The abstract asserts that known attacks are systematically reviewed with identified parameter regimes and limitations. That claim is load-bearing for the survey's usefulness. The full manuscript must supply explicit regime statements (e.g., asymptotic or concrete parameter ranges) and clear limitation discussions for each major attack family; absence or vagueness of those statements would undermine the central contribution and would need to be remedied.
minor comments (2)
- The abstract is clear and well-scoped. Once the full text is available, ensure that the claimed relationships among formulations and hardness assumptions are made explicit (e.g., via a comparison table or reduction diagram) so that the survey's organizational contribution is easy to extract.
- When the body is supplied, check that open problems are stated with enough precision (what is open, why existing techniques fail, and what would constitute progress) to be actionable rather than merely listed.
Circularity Check
No circularity: abstract-only survey with no derivation chain, fits, or load-bearing self-citations to inspect.
full rationale
The document is an abstract-only literature survey on the code equivalence problem. It claims to explain existing results, relationships among formulations/algorithms/hardness assumptions, review attacks and parameter regimes, and list open problems. There is no claimed first-principles derivation of a numerical prediction, no fitted parameter renamed as a prediction, no uniqueness theorem imported from the authors, and no ansatz smuggled via self-citation. A survey organizes prior work; its central claim is coverage and organization rather than a forced result. With only the abstract available, no equations, self-citations, or reductions can be exhibited. Per the hard rules, honest non-finding is required: score 0, empty steps. Minor expected self-citation risk in any survey is not circularity without a load-bearing reduction that can be quoted.
Axiom & Free-Parameter Ledger
axioms (2)
- domain assumption Standard definitions of linear codes and of code equivalence (permutation, monomial, or related variants) as used in the coding-theory literature.
- domain assumption Existing hardness assumptions and attack analyses in the cited literature are correctly stated and comparable across parameter regimes.
read the original abstract
In this work, we provide a comprehensive survey of the code equivalence problem and its variants. We explain the existing results, highlighting the relationships between different problem formulations, algorithmic techniques, and hardness assumptions. In addition, we systematically review known attacks, identify the parameter regimes in which they are effective, and discuss their limitations. Lastly, we outline several open problems and research directions, with the aim of clarifying the current landscape and guiding future work toward a deeper understanding of the hardness of code equivalence.
discussion (0)
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