Calculator Inputs
Enter block-code parameters below. The result appears above this form after submission.
Example Data Table
These sample rows help verify typical block-code behavior before entering custom values.
| Example | Family | q | n | k | d | Redundancy | Rate | Correctable | Detectable |
|---|---|---|---|---|---|---|---|---|---|
| Binary Hamming | (7,4,3) code | 2 | 7 | 4 | 3 | 3 | 0.571429 | 1 | 2 |
| Binary BCH | (15,7,5) code | 2 | 15 | 7 | 5 | 8 | 0.466667 | 2 | 4 |
| Binary Golay | (23,12,7) code | 2 | 23 | 12 | 7 | 11 | 0.521739 | 3 | 6 |
| Reed-Solomon style | (15,11,5) code | 16 | 15 | 11 | 5 | 4 | 0.733333 | 2 | 4 |
Formula Used
- Code rate:
R = k / n - Redundancy:
r = n - k - Guaranteed correction capability:
t = floor((d - 1) / 2) - Guaranteed detection capability:
s = d - 1 - Number of codewords:
M = q^k - Syndrome count:
q^(n-k) - Hamming sphere volume:
Vt = Σ C(n,i)(q-1)^ifori = 0tot - Hamming bound:
M ≤ q^n / Vt - Singleton bound:
M ≤ q^(n-d+1) - Guaranteed correctable block probability:
Σ C(n,i)p^i(1-p)^(n-i)fori = 0tot
How to Use This Calculator
- Choose a preset or enter custom values for n, k, d, and q.
- Enter a symbol error probability p to model channel reliability.
- Set the number of transmitted blocks to estimate expected successes and failures.
- Enter observed symbol errors to compare one received block against guaranteed limits.
- Click Calculate to view the result above the form, then export it as CSV or PDF.
FAQs
1. What does block length n represent?
It is the total number of transmitted symbols in one codeword. That total includes original information symbols and the redundant symbols added for protection.
2. What does message length k represent?
It is the number of information symbols carried by one codeword. Larger k often improves efficiency, while smaller k usually leaves more room for protection.
3. Why is minimum distance d so important?
Minimum distance sets the guaranteed detection and correction limits. A larger distance usually means stronger protection, though it may reduce rate or increase redundancy.
4. What does the correction result actually guarantee?
The calculator reports guarantees derived from minimum distance. A decoder may sometimes fix more errors, but the formula only marks what is always guaranteed.
5. Why can some errors be detectable but not correctable?
When the error count lies above the correction radius but below the detection limit, the receiver can usually notice corruption without knowing the unique original codeword.
6. What does the packing ratio mean?
It compares all correction spheres against the full q-ary space. A ratio above 1 suggests the entered parameters violate the Hamming packing bound.
7. Can I use q larger than 2?
Yes. Use larger q for nonbinary symbol codes, including many Reed-Solomon-style settings. In that case, p is interpreted as symbol error probability.
8. Why are some outputs shown in scientific notation?
Code spaces grow extremely fast. Scientific notation keeps huge values readable while preserving scale for codewords, syndrome counts, and theoretical bounds.