Information on Result #548397
There is no linear OA(2206, 215, F2, 104) (dual of [215, 9, 105]-code), because residual code would yield linear OA(2102, 110, F2, 52) (dual of [110, 8, 53]-code), but
- residual code [i] would yield linear OA(250, 57, F2, 26) (dual of [57, 7, 27]-code), but
- adding a parity check bit [i] would yield linear OA(251, 58, F2, 27) (dual of [58, 7, 28]-code), but
- “vT3†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(251, 58, F2, 27) (dual of [58, 7, 28]-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(2207, 216, F2, 105) (dual of [216, 9, 106]-code) | [i] | Truncation | |
| 2 | No linear OA(2208, 217, F2, 106) (dual of [217, 9, 107]-code) | [i] | ||
| 3 | No linear OA(2209, 218, F2, 107) (dual of [218, 9, 108]-code) | [i] | ||
| 4 | No linear OOA(2207, 215, F2, 2, 105) (dual of [(215, 2), 223, 106]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(2208, 215, F2, 2, 106) (dual of [(215, 2), 222, 107]-NRT-code) | [i] | ||
| 6 | No linear OOA(2209, 215, F2, 2, 107) (dual of [(215, 2), 221, 108]-NRT-code) | [i] | ||
| 7 | No linear OOA(2210, 215, F2, 2, 108) (dual of [(215, 2), 220, 109]-NRT-code) | [i] | ||
| 8 | No linear OOA(2211, 215, F2, 2, 109) (dual of [(215, 2), 219, 110]-NRT-code) | [i] | ||
| 9 | No linear OOA(2212, 215, F2, 2, 110) (dual of [(215, 2), 218, 111]-NRT-code) | [i] | ||
| 10 | No linear OOA(2213, 215, F2, 2, 111) (dual of [(215, 2), 217, 112]-NRT-code) | [i] | ||
| 11 | No linear OOA(2214, 215, F2, 2, 112) (dual of [(215, 2), 216, 113]-NRT-code) | [i] | ||
| 12 | No linear OOA(2215, 215, F2, 2, 113) (dual of [(215, 2), 215, 114]-NRT-code) | [i] | ||
| 13 | No linear OOA(2216, 215, F2, 2, 114) (dual of [(215, 2), 214, 115]-NRT-code) | [i] | ||
| 14 | No linear OOA(2217, 215, F2, 2, 115) (dual of [(215, 2), 213, 116]-NRT-code) | [i] | ||
| 15 | No linear OOA(2218, 215, F2, 2, 116) (dual of [(215, 2), 212, 117]-NRT-code) | [i] | ||
| 16 | No linear OOA(2219, 215, F2, 2, 117) (dual of [(215, 2), 211, 118]-NRT-code) | [i] | ||
| 17 | No linear OOA(2220, 215, F2, 2, 118) (dual of [(215, 2), 210, 119]-NRT-code) | [i] | ||
| 18 | No linear OOA(2221, 215, F2, 2, 119) (dual of [(215, 2), 209, 120]-NRT-code) | [i] | ||
| 19 | No linear OOA(2222, 215, F2, 2, 120) (dual of [(215, 2), 208, 121]-NRT-code) | [i] | ||
| 20 | No linear OOA(2223, 215, F2, 2, 121) (dual of [(215, 2), 207, 122]-NRT-code) | [i] | ||
| 21 | No linear OOA(2224, 215, F2, 2, 122) (dual of [(215, 2), 206, 123]-NRT-code) | [i] | ||
| 22 | No linear OOA(2225, 215, F2, 2, 123) (dual of [(215, 2), 205, 124]-NRT-code) | [i] | ||
| 23 | No linear OOA(2226, 215, F2, 2, 124) (dual of [(215, 2), 204, 125]-NRT-code) | [i] | ||
| 24 | No linear OOA(2227, 215, F2, 2, 125) (dual of [(215, 2), 203, 126]-NRT-code) | [i] | ||
| 25 | No linear OOA(2228, 215, F2, 2, 126) (dual of [(215, 2), 202, 127]-NRT-code) | [i] | ||
| 26 | No linear OOA(2229, 215, F2, 2, 127) (dual of [(215, 2), 201, 128]-NRT-code) | [i] | ||
| 27 | No linear OOA(2230, 215, F2, 2, 128) (dual of [(215, 2), 200, 129]-NRT-code) | [i] | ||
| 28 | No linear OOA(2231, 215, F2, 2, 129) (dual of [(215, 2), 199, 130]-NRT-code) | [i] | ||
| 29 | No linear OOA(2232, 215, F2, 2, 130) (dual of [(215, 2), 198, 131]-NRT-code) | [i] | ||
| 30 | No linear OOA(2233, 215, F2, 2, 131) (dual of [(215, 2), 197, 132]-NRT-code) | [i] | ||
| 31 | No linear OOA(2234, 215, F2, 2, 132) (dual of [(215, 2), 196, 133]-NRT-code) | [i] | ||
| 32 | No linear OOA(2235, 215, F2, 2, 133) (dual of [(215, 2), 195, 134]-NRT-code) | [i] | ||
| 33 | No linear OOA(2236, 215, F2, 2, 134) (dual of [(215, 2), 194, 135]-NRT-code) | [i] | ||
| 34 | No linear OOA(2237, 215, F2, 2, 135) (dual of [(215, 2), 193, 136]-NRT-code) | [i] | ||
| 35 | No linear OOA(2238, 215, F2, 2, 136) (dual of [(215, 2), 192, 137]-NRT-code) | [i] | ||
| 36 | No linear OOA(2239, 215, F2, 2, 137) (dual of [(215, 2), 191, 138]-NRT-code) | [i] | ||
| 37 | No linear OOA(2240, 215, F2, 2, 138) (dual of [(215, 2), 190, 139]-NRT-code) | [i] | ||
| 38 | No linear OOA(2241, 215, F2, 2, 139) (dual of [(215, 2), 189, 140]-NRT-code) | [i] | ||
| 39 | No linear OOA(2242, 215, F2, 2, 140) (dual of [(215, 2), 188, 141]-NRT-code) | [i] | ||
| 40 | No linear OOA(2243, 215, F2, 2, 141) (dual of [(215, 2), 187, 142]-NRT-code) | [i] | ||
| 41 | No linear OOA(2244, 215, F2, 2, 142) (dual of [(215, 2), 186, 143]-NRT-code) | [i] | ||
| 42 | No linear OOA(2245, 215, F2, 2, 143) (dual of [(215, 2), 185, 144]-NRT-code) | [i] | ||
| 43 | No linear OOA(2246, 215, F2, 2, 144) (dual of [(215, 2), 184, 145]-NRT-code) | [i] | ||
| 44 | No linear OOA(2247, 215, F2, 2, 145) (dual of [(215, 2), 183, 146]-NRT-code) | [i] | ||
| 45 | No linear OOA(2248, 215, F2, 2, 146) (dual of [(215, 2), 182, 147]-NRT-code) | [i] | ||
| 46 | No linear OOA(2249, 215, F2, 2, 147) (dual of [(215, 2), 181, 148]-NRT-code) | [i] | ||
| 47 | No linear OOA(2250, 215, F2, 2, 148) (dual of [(215, 2), 180, 149]-NRT-code) | [i] | ||
| 48 | No linear OOA(2251, 215, F2, 2, 149) (dual of [(215, 2), 179, 150]-NRT-code) | [i] | ||
| 49 | No linear OOA(2252, 215, F2, 2, 150) (dual of [(215, 2), 178, 151]-NRT-code) | [i] | ||
| 50 | No linear OOA(2253, 215, F2, 2, 151) (dual of [(215, 2), 177, 152]-NRT-code) | [i] | ||
| 51 | No linear OOA(2254, 215, F2, 2, 152) (dual of [(215, 2), 176, 153]-NRT-code) | [i] | ||
| 52 | No linear OOA(2255, 215, F2, 2, 153) (dual of [(215, 2), 175, 154]-NRT-code) | [i] | ||
| 53 | No linear OOA(2256, 215, F2, 2, 154) (dual of [(215, 2), 174, 155]-NRT-code) | [i] | ||
| 54 | No linear OOA(2257, 215, F2, 2, 155) (dual of [(215, 2), 173, 156]-NRT-code) | [i] | ||
| 55 | No linear OOA(2258, 215, F2, 2, 156) (dual of [(215, 2), 172, 157]-NRT-code) | [i] | ||
| 56 | No linear OOA(2259, 215, F2, 2, 157) (dual of [(215, 2), 171, 158]-NRT-code) | [i] | ||
| 57 | No linear OOA(2260, 215, F2, 2, 158) (dual of [(215, 2), 170, 159]-NRT-code) | [i] | ||
| 58 | No linear OOA(2206, 215, F2, 2, 104) (dual of [(215, 2), 224, 105]-NRT-code) | [i] | Depth Reduction | |
| 59 | No linear OOA(2206, 215, F2, 3, 104) (dual of [(215, 3), 439, 105]-NRT-code) | [i] | ||
| 60 | No linear OOA(2206, 215, F2, 4, 104) (dual of [(215, 4), 654, 105]-NRT-code) | [i] | ||
| 61 | No linear OOA(2206, 215, F2, 5, 104) (dual of [(215, 5), 869, 105]-NRT-code) | [i] | ||
| 62 | No linear OOA(2206, 215, F2, 6, 104) (dual of [(215, 6), 1084, 105]-NRT-code) | [i] | ||
| 63 | No linear OOA(2206, 215, F2, 7, 104) (dual of [(215, 7), 1299, 105]-NRT-code) | [i] | ||
| 64 | No linear OOA(2206, 215, F2, 8, 104) (dual of [(215, 8), 1514, 105]-NRT-code) | [i] | ||
| 65 | No digital (102, 206, 215)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |