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coding_theory_operation

Compute error-correcting code parameters: length, dimension, minimum distance, rate, and generator matrix for Hamming and generalized Reed-Solomon codes.

Instructions

Error-correcting codes: length, dimension, minimum distance, rate and generator matrix for Hamming and generalized Reed-Solomon codes. Prefer this over evaluate_sage for code parameters.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
sessionNoNamed workspace to use. Workspaces have independent variables; omit for 'default'.default
code_typeYesCode constructor, e.g. 'HammingCode(GF(2),3)', 'GeneralizedReedSolomonCode(GF(7).list()[:6],3)'
operationYesOne of: length, dimension, minimum_distance, generator_matrix, rate

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault

No arguments

Behavior2/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description must carry the full burden of behavioral disclosure. It only states what the tool computes but does not mention any side effects, session behavior, error conditions, or execution details (e.g., whether it modifies state or requires a running Sage session). This is a significant gap for a tool with no annotation safety hints.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is exactly two sentences. The first efficiently lists the tool's scope, and the second provides a clear usage preference. Every word earns its place with no fluff or redundancy.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the presence of a full input schema, an output schema, and the tool's moderate complexity, the description covers the core functionality and gives a usage hint. It could be more complete by addressing session behavior or edge cases, but the structured schemas fill most gaps. The description is sufficiently complete for an agent to correctly select and invoke the tool for most coding theory parameter queries.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%—all three parameters (session, code_type, operation) have descriptions with examples. The tool description adds context about the code families and operations, but this largely mirrors the schema's own descriptions and adds limited new semantic value beyond what is already structured.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool computes error-correcting code parameters (length, dimension, minimum distance, rate, generator matrix) for Hamming and generalized Reed-Solomon codes. It uses a specific verb ('compute' implied), names the resource (codes), and distinguishes itself from the sibling tool evaluate_sage.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description gives explicit guidance to prefer this tool over evaluate_sage for code parameters, naming the alternative. However, it does not explicitly state when not to use this tool (e.g., for non-code computations or other code families), so it falls slightly short of a 5.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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