CRC Polynomial Reversal Tool
Reverse all coefficients of a full monic CRC polynomial with nonzero constant coefficient to obtain its reciprocal; includes the leading coefficient.
Description
Reverse all coefficients of a full monic CRC polynomial with nonzero constant coefficient to obtain its reciprocal; includes the leading coefficient.
A reciprocal polynomial reverses all coefficients through its declared degree. Here the integer representation includes the leading and constant coefficients.
When to use this tool
Reverse all coefficients of a full monic CRC polynomial with nonzero constant coefficient to obtain its reciprocal; includes the leading coefficient.
- Prepare the supplied polynomial, degree 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 polynomial, degree. 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.reciprocalPolynomial. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Require degree 1 to 128 and polynomial between 2^degree and 2^(degree+1), with an odd constant bit. Reverse degree plus one bits and return reciprocalPolynomial as decimal text.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| 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 |
| degree | degree. | Integer from 1 to 128 inclusive |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.reciprocalPolynomial | The reciprocal polynomial value under the stated formula or text convention. |
{
"input": {
"polynomial": "19",
"degree": 4
},
"output": {
"result": {
"reciprocalPolynomial": "25"
}
}
}Limitations and assumptions
- This convention differs from CRC parameter records that omit the leading coefficient. No payload CRC or polynomial-strength analysis is performed.
- 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
Similar or alternative tools
- 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.
- CRC Parameter Record Audit
Audit explicit CRC parameter width evidence under the omitted-leading-coefficient convention; no CRC computation, polynomial quality or catalog identification.