Information on Result #548409
There is no linear OA(2224, 236, F2, 112) (dual of [236, 12, 113]-code), because residual code would yield linear OA(2112, 123, F2, 56) (dual of [123, 11, 57]-code), but
- residual code [i] would yield linear OA(256, 66, F2, 28) (dual of [66, 10, 29]-code), but
- adding a parity check bit [i] would yield linear OA(257, 67, F2, 29) (dual of [67, 10, 30]-code), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(2225, 237, F2, 113) (dual of [237, 12, 114]-code) | [i] | Truncation | |
| 2 | No linear OOA(2225, 236, F2, 2, 113) (dual of [(236, 2), 247, 114]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2227, 236, F2, 2, 115) (dual of [(236, 2), 245, 116]-NRT-code) | [i] | ||
| 4 | No linear OOA(2228, 236, F2, 2, 116) (dual of [(236, 2), 244, 117]-NRT-code) | [i] | ||
| 5 | No linear OOA(2229, 236, F2, 2, 117) (dual of [(236, 2), 243, 118]-NRT-code) | [i] | ||
| 6 | No linear OOA(2230, 236, F2, 2, 118) (dual of [(236, 2), 242, 119]-NRT-code) | [i] | ||
| 7 | No linear OOA(2231, 236, F2, 2, 119) (dual of [(236, 2), 241, 120]-NRT-code) | [i] | ||
| 8 | No linear OOA(2232, 236, F2, 2, 120) (dual of [(236, 2), 240, 121]-NRT-code) | [i] | ||
| 9 | No linear OOA(2233, 236, F2, 2, 121) (dual of [(236, 2), 239, 122]-NRT-code) | [i] | ||
| 10 | No linear OOA(2234, 236, F2, 2, 122) (dual of [(236, 2), 238, 123]-NRT-code) | [i] | ||
| 11 | No linear OOA(2235, 236, F2, 2, 123) (dual of [(236, 2), 237, 124]-NRT-code) | [i] | ||
| 12 | No linear OOA(2236, 236, F2, 2, 124) (dual of [(236, 2), 236, 125]-NRT-code) | [i] | ||
| 13 | No linear OOA(2237, 236, F2, 2, 125) (dual of [(236, 2), 235, 126]-NRT-code) | [i] | ||
| 14 | No linear OOA(2238, 236, F2, 2, 126) (dual of [(236, 2), 234, 127]-NRT-code) | [i] | ||
| 15 | No linear OOA(2239, 236, F2, 2, 127) (dual of [(236, 2), 233, 128]-NRT-code) | [i] | ||
| 16 | No linear OOA(2240, 236, F2, 2, 128) (dual of [(236, 2), 232, 129]-NRT-code) | [i] | ||
| 17 | No linear OOA(2241, 236, F2, 2, 129) (dual of [(236, 2), 231, 130]-NRT-code) | [i] | ||
| 18 | No linear OOA(2242, 236, F2, 2, 130) (dual of [(236, 2), 230, 131]-NRT-code) | [i] | ||
| 19 | No linear OOA(2243, 236, F2, 2, 131) (dual of [(236, 2), 229, 132]-NRT-code) | [i] | ||
| 20 | No linear OOA(2244, 236, F2, 2, 132) (dual of [(236, 2), 228, 133]-NRT-code) | [i] | ||
| 21 | No linear OOA(2245, 236, F2, 2, 133) (dual of [(236, 2), 227, 134]-NRT-code) | [i] | ||
| 22 | No linear OOA(2246, 236, F2, 2, 134) (dual of [(236, 2), 226, 135]-NRT-code) | [i] | ||
| 23 | No linear OOA(2247, 236, F2, 2, 135) (dual of [(236, 2), 225, 136]-NRT-code) | [i] | ||
| 24 | No linear OOA(2248, 236, F2, 2, 136) (dual of [(236, 2), 224, 137]-NRT-code) | [i] | ||
| 25 | No linear OOA(2249, 236, F2, 2, 137) (dual of [(236, 2), 223, 138]-NRT-code) | [i] | ||
| 26 | No linear OOA(2250, 236, F2, 2, 138) (dual of [(236, 2), 222, 139]-NRT-code) | [i] | ||
| 27 | No linear OOA(2251, 236, F2, 2, 139) (dual of [(236, 2), 221, 140]-NRT-code) | [i] | ||
| 28 | No linear OOA(2252, 236, F2, 2, 140) (dual of [(236, 2), 220, 141]-NRT-code) | [i] | ||
| 29 | No linear OOA(2253, 236, F2, 2, 141) (dual of [(236, 2), 219, 142]-NRT-code) | [i] | ||
| 30 | No linear OOA(2254, 236, F2, 2, 142) (dual of [(236, 2), 218, 143]-NRT-code) | [i] | ||
| 31 | No linear OOA(2255, 236, F2, 2, 143) (dual of [(236, 2), 217, 144]-NRT-code) | [i] | ||
| 32 | No linear OOA(2256, 236, F2, 2, 144) (dual of [(236, 2), 216, 145]-NRT-code) | [i] | ||
| 33 | No linear OOA(2257, 236, F2, 2, 145) (dual of [(236, 2), 215, 146]-NRT-code) | [i] | ||
| 34 | No linear OOA(2258, 236, F2, 2, 146) (dual of [(236, 2), 214, 147]-NRT-code) | [i] | ||
| 35 | No linear OOA(2259, 236, F2, 2, 147) (dual of [(236, 2), 213, 148]-NRT-code) | [i] | ||
| 36 | No linear OOA(2260, 236, F2, 2, 148) (dual of [(236, 2), 212, 149]-NRT-code) | [i] | ||
| 37 | No linear OOA(2224, 236, F2, 2, 112) (dual of [(236, 2), 248, 113]-NRT-code) | [i] | Depth Reduction | |
| 38 | No linear OOA(2224, 236, F2, 3, 112) (dual of [(236, 3), 484, 113]-NRT-code) | [i] | ||
| 39 | No linear OOA(2224, 236, F2, 4, 112) (dual of [(236, 4), 720, 113]-NRT-code) | [i] | ||
| 40 | No linear OOA(2224, 236, F2, 5, 112) (dual of [(236, 5), 956, 113]-NRT-code) | [i] | ||
| 41 | No linear OOA(2224, 236, F2, 6, 112) (dual of [(236, 6), 1192, 113]-NRT-code) | [i] | ||
| 42 | No linear OOA(2224, 236, F2, 7, 112) (dual of [(236, 7), 1428, 113]-NRT-code) | [i] | ||
| 43 | No linear OOA(2224, 236, F2, 8, 112) (dual of [(236, 8), 1664, 113]-NRT-code) | [i] | ||
| 44 | No digital (112, 224, 236)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |