CRC Parameter Record Audit

Audit explicit CRC parameter width evidence under the omitted-leading-coefficient convention; no CRC computation, polynomial quality or catalog identification.

Description

Audit explicit CRC parameter width evidence under the omitted-leading-coefficient convention; no CRC computation, polynomial quality or catalog identification.

A CRC parameter record needs a declared width and an explicit polynomial convention. Fitting the fields is distinct from computing or endorsing a CRC.

When to use this tool

Audit explicit CRC parameter width evidence under the omitted-leading-coefficient convention; no CRC computation, polynomial quality or catalog identification.

Prepare the supplied width, polynomial, initial, xorOut, reflectIn, reflectOut fields for this operation.
Compare the complete example with the representation used by your own input before carrying the result into another step.

How to use the tool and how it works

Enter width, polynomial, initial, xorOut, reflectIn, reflectOut. Use the exact text syntax, units and index conventions explained below.
Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
Read result.withinWidth, result.polynomialHasConstant, result.reflectIn, result.reflectOut, result.convention. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.

For width 1 to 128, parse polynomial, initial and xorOut as exact integers and return three withinWidth flags for [0, 2^width). Report whether the polynomial is nonnegative and odd, echo reflection flags and state that its leading coefficient is excluded.^[1]

Input field	Meaning and representation	Accepted input
width	width.	Integer from 1 to 128 inclusive
polynomial	Exact decimal integer text; keep it quoted in JSON rather than converting through a floating-point number.	Optional leading + or - and 1 to 256 decimal digits; no whitespace
initial	Exact decimal integer text; keep it quoted in JSON rather than converting through a floating-point number.	Optional leading + or - and 1 to 256 decimal digits; no whitespace
xorOut	Exact decimal integer text; keep it quoted in JSON rather than converting through a floating-point number.	Optional leading + or - and 1 to 256 decimal digits; no whitespace
reflectIn	Explicit choice for reflect in; supply a boolean rather than a text label.	true or false
reflectOut	Explicit choice for reflect out; supply a boolean rather than a text label.	true or false

Output field	Interpretation
result	Object containing the named outputs below.
result.withinWidth	The within width list in the ordering and representation described above.
result.polynomialHasConstant	Flag for polynomial has constant under the exact condition described above.
result.reflectIn	Flag for reflect in under the exact condition described above.
result.reflectOut	Flag for reflect out under the exact condition described above.
result.convention	The convention value under the stated formula or text convention.

json

{
  "input": {
    "width": 4,
    "polynomial": "3",
    "initial": "16",
    "xorOut": "0",
    "reflectIn": false,
    "reflectOut": false
  },
  "output": {
    "result": {
      "withinWidth": [
        true,
        false,
        true
      ],
      "polynomialHasConstant": true,
      "reflectIn": false,
      "reflectOut": false,
      "convention": "polynomial excludes leading coefficient"
    }
  }
}

Limitations and assumptions

Out-of-width fields produce flags rather than a CRC result. Polynomial quality, algorithm compatibility and test vectors are not verified.
All declared input fields are required and unexpected top-level fields are rejected. Numbers must be finite; lists are limited to 128 entries and ordinary text fields to 8,192 UTF-16 code units, with tighter limits where stated.
JSON text inputs must parse within bounded nesting and size limits. Numeric outputs outside the safe finite range are rejected; large exact integer results use decimal strings. Indexes and half-open spans are zero-based unless a rank is explicitly described as one-based.

Alternative or Complementary methods

Use the complete specified checksum algorithm and independent test vectors when verifying a payload. Field packing, parameter shape and arithmetic agreement are separate checks; none supplies cryptographic authenticity.

References

Tool behavior and example: CRC Parameter Record Audit — tool.io

Similar or alternative tools

Checksum Record Width Audit
Audit exact checksum-record integer values against an explicit unsigned bit width; report range failures while rejecting malformed integer spellings.
CRC Polynomial Degree Check
Audit the degree and constant coefficient of a full CRC GF(2) polynomial integer including its leading coefficient; not an omitted-leading-bit parameter.