FA-72301 / Error-correcting codes / Open access
RS framing always adds a codeword · case 01
Payloads that are an exact multiple of k (and empty payloads) get an extra, empty codeword.
ROOT CAUSE
The count is payload // k + 1 instead of the ceiling.
VERIFIED REPAIR
Use ceil(payload / k).
Unsuccessful approach: Plain floor division drops the partial last codeword.
Case contract
Frame a payload of the given number of bytes into shortened RS(n, k) codewords: cw = ceil(payload / k) codewords, the last one carries payload - (cw - 1)*k data bytes (shortened, zero padding not transmitted), and each codeword adds n - k parity bytes. An empty payload uses no codewords. Return [cw, last data bytes, bytes sent]; invalid parameters return None.
Why this case matters
Link layers size FEC frames and transmit budgets from the payload length.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(payload, n, k):
if payload < 0 or not 0 < k < n:
return None
cw = payload // k + 1
last = payload - (cw - 1) * k if cw else 0
sent = payload + cw * (n - k)
return [cw, last, sent]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [0, 255, 239]', [0, 255, 239], [0, 0, 0]], ['regression [239, 255, 239]', [239, 255, 239], [1, 239, 255]], ['partial-repair [1, 255, 239]', [1, 255, 239], [1, 1, 17]], ['partial-repair [240, 255, 239]', [240, 255, 239], [2, 1, 272]], ['control [-1, 15, 11]', [-1, 15, 11], None], ['control [5, 11, 11]', [5, 11, 11], None], ['control [478, 255, 239]', [478, 255, 239], [2, 239, 510]], ['control [1000, 255, 223]', [1000, 255, 223], [5, 108, 1160]]], [['regression [223, 255, 223]', [223, 255, 223], [1, 223, 255]], ['regression [11, 15, 11]', [11, 15, 11], [1, 11, 15]], ['partial-repair [5, 15, 11]', [5, 15, 11], [1, 5, 9]], ['partial-repair [12, 15, 11]', [12, 15, 11], [2, 1, 20]], ['control [5, 11, 11]', [5, 11, 11], None], ['control [-1, 15, 11]', [-1, 15, 11], None], ['control [33, 15, 11]', [33, 15, 11], [3, 11, 45]], ['control [100, 204, 188]', [100, 204, 188], [1, 100, 116]]], [['regression [188, 204, 188]', [188, 204, 188], [1, 188, 204]], ['regression [376, 204, 188]', [376, 204, 188], [2, 188, 408]], ['partial-repair [22, 7, 4]', [22, 7, 4], [6, 2, 40]], ['partial-repair [1, 7, 4]', [1, 7, 4], [1, 1, 4]], ['control [-1, 15, 11]', [-1, 15, 11], None], ['control [5, 11, 11]', [5, 11, 11], None], ['control [0, 255, 239]', [0, 255, 239], [0, 0, 0]], ['control [1, 255, 239]', [1, 255, 239], [1, 1, 17]]], [['regression [239, 255, 239]', [239, 255, 239], [1, 239, 255]], ['regression [478, 255, 239]', [478, 255, 239], [2, 239, 510]], ['partial-repair [240, 255, 239]', [240, 255, 239], [2, 1, 272]], ['partial-repair [1000, 255, 223]', [1000, 255, 223], [5, 108, 1160]], ['control [5, 11, 11]', [5, 11, 11], None], ['control [-1, 15, 11]', [-1, 15, 11], None], ['control [1, 7, 4]', [1, 7, 4], [1, 1, 4]], ['control [0, 255, 239]', [0, 255, 239], [0, 0, 0]]], [['regression [11, 15, 11]', [11, 15, 11], [1, 11, 15]], ['regression [33, 15, 11]', [33, 15, 11], [3, 11, 45]], ['partial-repair [12, 15, 11]', [12, 15, 11], [2, 1, 20]], ['partial-repair [100, 204, 188]', [100, 204, 188], [1, 100, 116]], ['control [-1, 15, 11]', [-1, 15, 11], None], ['control [5, 11, 11]', [5, 11, 11], None], ['control [478, 255, 239]', [478, 255, 239], [2, 239, 510]], ['control [1000, 255, 223]', [1000, 255, 223], [5, 108, 1160]]]]
for label, args, expected in fixtures[N - 1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression [0, 255, 239] | [1, 0, 16] | [0, 0, 0] | Failed |
| regression [239, 255, 239] | [2, 0, 271] | [1, 239, 255] | Failed |
| partial-repair [1, 255, 239] | [1, 1, 17] | [1, 1, 17] | Passed |
| partial-repair [240, 255, 239] | [2, 1, 272] | [2, 1, 272] | Passed |
| control [-1, 15, 11] | None | None | Passed |
| control [5, 11, 11] | None | None | Passed |
| control [478, 255, 239] | [3, 0, 526] | [2, 239, 510] | Failed |
| control [1000, 255, 223] | [5, 108, 1160] | [5, 108, 1160] | Passed |
SHA-256 / 98d2fb45a5a534b0f898ff53e5a11126e2529c0d6ab00bdf68f7371262245706
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(payload, n, k):
if payload < 0 or not 0 < k < n:
return None
cw = payload // k
last = payload - (cw - 1) * k if cw else 0
sent = payload + cw * (n - k)
return [cw, last, sent]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [0, 255, 239]', [0, 255, 239], [0, 0, 0]], ['regression [239, 255, 239]', [239, 255, 239], [1, 239, 255]], ['partial-repair [1, 255, 239]', [1, 255, 239], [1, 1, 17]], ['partial-repair [240, 255, 239]', [240, 255, 239], [2, 1, 272]], ['control [-1, 15, 11]', [-1, 15, 11], None], ['control [5, 11, 11]', [5, 11, 11], None], ['control [478, 255, 239]', [478, 255, 239], [2, 239, 510]], ['control [1000, 255, 223]', [1000, 255, 223], [5, 108, 1160]]], [['regression [223, 255, 223]', [223, 255, 223], [1, 223, 255]], ['regression [11, 15, 11]', [11, 15, 11], [1, 11, 15]], ['partial-repair [5, 15, 11]', [5, 15, 11], [1, 5, 9]], ['partial-repair [12, 15, 11]', [12, 15, 11], [2, 1, 20]], ['control [5, 11, 11]', [5, 11, 11], None], ['control [-1, 15, 11]', [-1, 15, 11], None], ['control [33, 15, 11]', [33, 15, 11], [3, 11, 45]], ['control [100, 204, 188]', [100, 204, 188], [1, 100, 116]]], [['regression [188, 204, 188]', [188, 204, 188], [1, 188, 204]], ['regression [376, 204, 188]', [376, 204, 188], [2, 188, 408]], ['partial-repair [22, 7, 4]', [22, 7, 4], [6, 2, 40]], ['partial-repair [1, 7, 4]', [1, 7, 4], [1, 1, 4]], ['control [-1, 15, 11]', [-1, 15, 11], None], ['control [5, 11, 11]', [5, 11, 11], None], ['control [0, 255, 239]', [0, 255, 239], [0, 0, 0]], ['control [1, 255, 239]', [1, 255, 239], [1, 1, 17]]], [['regression [239, 255, 239]', [239, 255, 239], [1, 239, 255]], ['regression [478, 255, 239]', [478, 255, 239], [2, 239, 510]], ['partial-repair [240, 255, 239]', [240, 255, 239], [2, 1, 272]], ['partial-repair [1000, 255, 223]', [1000, 255, 223], [5, 108, 1160]], ['control [5, 11, 11]', [5, 11, 11], None], ['control [-1, 15, 11]', [-1, 15, 11], None], ['control [1, 7, 4]', [1, 7, 4], [1, 1, 4]], ['control [0, 255, 239]', [0, 255, 239], [0, 0, 0]]], [['regression [11, 15, 11]', [11, 15, 11], [1, 11, 15]], ['regression [33, 15, 11]', [33, 15, 11], [3, 11, 45]], ['partial-repair [12, 15, 11]', [12, 15, 11], [2, 1, 20]], ['partial-repair [100, 204, 188]', [100, 204, 188], [1, 100, 116]], ['control [-1, 15, 11]', [-1, 15, 11], None], ['control [5, 11, 11]', [5, 11, 11], None], ['control [478, 255, 239]', [478, 255, 239], [2, 239, 510]], ['control [1000, 255, 223]', [1000, 255, 223], [5, 108, 1160]]]]
for label, args, expected in fixtures[N - 1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression [0, 255, 239] | [0, 0, 0] | [0, 0, 0] | Passed |
| regression [239, 255, 239] | [1, 239, 255] | [1, 239, 255] | Passed |
| partial-repair [1, 255, 239] | [0, 0, 1] | [1, 1, 17] | Failed |
| partial-repair [240, 255, 239] | [1, 240, 256] | [2, 1, 272] | Failed |
| control [-1, 15, 11] | None | None | Passed |
| control [5, 11, 11] | None | None | Passed |
| control [478, 255, 239] | [2, 239, 510] | [2, 239, 510] | Passed |
| control [1000, 255, 223] | [4, 331, 1128] | [5, 108, 1160] | Failed |
SHA-256 / f8781d72d85faefe8f37d94bc6e684a692507beb78366cb2ae7d3eee315b7a2b
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(payload, n, k):
if payload < 0 or not 0 < k < n:
return None
cw = -(-payload // k)
last = payload - (cw - 1) * k if cw else 0
sent = payload + cw * (n - k)
return [cw, last, sent]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [0, 255, 239]', [0, 255, 239], [0, 0, 0]], ['regression [239, 255, 239]', [239, 255, 239], [1, 239, 255]], ['partial-repair [1, 255, 239]', [1, 255, 239], [1, 1, 17]], ['partial-repair [240, 255, 239]', [240, 255, 239], [2, 1, 272]], ['control [-1, 15, 11]', [-1, 15, 11], None], ['control [5, 11, 11]', [5, 11, 11], None], ['control [478, 255, 239]', [478, 255, 239], [2, 239, 510]], ['control [1000, 255, 223]', [1000, 255, 223], [5, 108, 1160]]], [['regression [223, 255, 223]', [223, 255, 223], [1, 223, 255]], ['regression [11, 15, 11]', [11, 15, 11], [1, 11, 15]], ['partial-repair [5, 15, 11]', [5, 15, 11], [1, 5, 9]], ['partial-repair [12, 15, 11]', [12, 15, 11], [2, 1, 20]], ['control [5, 11, 11]', [5, 11, 11], None], ['control [-1, 15, 11]', [-1, 15, 11], None], ['control [33, 15, 11]', [33, 15, 11], [3, 11, 45]], ['control [100, 204, 188]', [100, 204, 188], [1, 100, 116]]], [['regression [188, 204, 188]', [188, 204, 188], [1, 188, 204]], ['regression [376, 204, 188]', [376, 204, 188], [2, 188, 408]], ['partial-repair [22, 7, 4]', [22, 7, 4], [6, 2, 40]], ['partial-repair [1, 7, 4]', [1, 7, 4], [1, 1, 4]], ['control [-1, 15, 11]', [-1, 15, 11], None], ['control [5, 11, 11]', [5, 11, 11], None], ['control [0, 255, 239]', [0, 255, 239], [0, 0, 0]], ['control [1, 255, 239]', [1, 255, 239], [1, 1, 17]]], [['regression [239, 255, 239]', [239, 255, 239], [1, 239, 255]], ['regression [478, 255, 239]', [478, 255, 239], [2, 239, 510]], ['partial-repair [240, 255, 239]', [240, 255, 239], [2, 1, 272]], ['partial-repair [1000, 255, 223]', [1000, 255, 223], [5, 108, 1160]], ['control [5, 11, 11]', [5, 11, 11], None], ['control [-1, 15, 11]', [-1, 15, 11], None], ['control [1, 7, 4]', [1, 7, 4], [1, 1, 4]], ['control [0, 255, 239]', [0, 255, 239], [0, 0, 0]]], [['regression [11, 15, 11]', [11, 15, 11], [1, 11, 15]], ['regression [33, 15, 11]', [33, 15, 11], [3, 11, 45]], ['partial-repair [12, 15, 11]', [12, 15, 11], [2, 1, 20]], ['partial-repair [100, 204, 188]', [100, 204, 188], [1, 100, 116]], ['control [-1, 15, 11]', [-1, 15, 11], None], ['control [5, 11, 11]', [5, 11, 11], None], ['control [478, 255, 239]', [478, 255, 239], [2, 239, 510]], ['control [1000, 255, 223]', [1000, 255, 223], [5, 108, 1160]]]]
for label, args, expected in fixtures[N - 1]:
check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression [0, 255, 239] | [0, 0, 0] | [0, 0, 0] | Passed |
| regression [239, 255, 239] | [1, 239, 255] | [1, 239, 255] | Passed |
| partial-repair [1, 255, 239] | [1, 1, 17] | [1, 1, 17] | Passed |
| partial-repair [240, 255, 239] | [2, 1, 272] | [2, 1, 272] | Passed |
| control [-1, 15, 11] | None | None | Passed |
| control [5, 11, 11] | None | None | Passed |
| control [478, 255, 239] | [2, 239, 510] | [2, 239, 510] | Passed |
| control [1000, 255, 223] | [5, 108, 1160] | [5, 108, 1160] | Passed |
SHA-256 / 0bfb8f3caaa0c11f5a47d73e5d4a63a3ccb49d3575c76b12f3643bf7eddaecc0
Verification & scope
A deterministic, bounded teaching model of the named code under the stated contract; not a production codec. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:48:37.314041+00:00.
Case digest / 1730c1ce6eed73f84d2d5f049c86a068f062dfac051736d94f7f0b6e464a260c