Information on Result #548323
There is no linear OA(2135, 144, F2, 68) (dual of [144, 9, 69]-code), because residual code would yield linear OA(267, 75, F2, 34) (dual of [75, 8, 35]-code), but
- adding a parity check bit [i] would yield linear OA(268, 76, F2, 35) (dual of [76, 8, 36]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
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(2136, 145, F2, 69) (dual of [145, 9, 70]-code) | [i] | Truncation | |
| 2 | No linear OOA(2136, 144, F2, 2, 69) (dual of [(144, 2), 152, 70]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2137, 144, F2, 2, 70) (dual of [(144, 2), 151, 71]-NRT-code) | [i] | ||
| 4 | No linear OOA(2138, 144, F2, 2, 71) (dual of [(144, 2), 150, 72]-NRT-code) | [i] | ||
| 5 | No linear OOA(2139, 144, F2, 2, 72) (dual of [(144, 2), 149, 73]-NRT-code) | [i] | ||
| 6 | No linear OOA(2140, 144, F2, 2, 73) (dual of [(144, 2), 148, 74]-NRT-code) | [i] | ||
| 7 | No linear OOA(2141, 144, F2, 2, 74) (dual of [(144, 2), 147, 75]-NRT-code) | [i] | ||
| 8 | No linear OOA(2142, 144, F2, 2, 75) (dual of [(144, 2), 146, 76]-NRT-code) | [i] | ||
| 9 | No linear OOA(2143, 144, F2, 2, 76) (dual of [(144, 2), 145, 77]-NRT-code) | [i] | ||
| 10 | No linear OOA(2144, 144, F2, 2, 77) (dual of [(144, 2), 144, 78]-NRT-code) | [i] | ||
| 11 | No linear OOA(2145, 144, F2, 2, 78) (dual of [(144, 2), 143, 79]-NRT-code) | [i] | ||
| 12 | No linear OOA(2146, 144, F2, 2, 79) (dual of [(144, 2), 142, 80]-NRT-code) | [i] | ||
| 13 | No linear OOA(2147, 144, F2, 2, 80) (dual of [(144, 2), 141, 81]-NRT-code) | [i] | ||
| 14 | No linear OOA(2148, 144, F2, 2, 81) (dual of [(144, 2), 140, 82]-NRT-code) | [i] | ||
| 15 | No linear OOA(2149, 144, F2, 2, 82) (dual of [(144, 2), 139, 83]-NRT-code) | [i] | ||
| 16 | No linear OOA(2150, 144, F2, 2, 83) (dual of [(144, 2), 138, 84]-NRT-code) | [i] | ||
| 17 | No linear OOA(2151, 144, F2, 2, 84) (dual of [(144, 2), 137, 85]-NRT-code) | [i] | ||
| 18 | No linear OOA(2152, 144, F2, 2, 85) (dual of [(144, 2), 136, 86]-NRT-code) | [i] | ||
| 19 | No linear OOA(2153, 144, F2, 2, 86) (dual of [(144, 2), 135, 87]-NRT-code) | [i] | ||
| 20 | No linear OOA(2154, 144, F2, 2, 87) (dual of [(144, 2), 134, 88]-NRT-code) | [i] | ||
| 21 | No linear OOA(2155, 144, F2, 2, 88) (dual of [(144, 2), 133, 89]-NRT-code) | [i] | ||
| 22 | No linear OOA(2156, 144, F2, 2, 89) (dual of [(144, 2), 132, 90]-NRT-code) | [i] | ||
| 23 | No linear OOA(2157, 144, F2, 2, 90) (dual of [(144, 2), 131, 91]-NRT-code) | [i] | ||
| 24 | No linear OOA(2158, 144, F2, 2, 91) (dual of [(144, 2), 130, 92]-NRT-code) | [i] | ||
| 25 | No linear OOA(2159, 144, F2, 2, 92) (dual of [(144, 2), 129, 93]-NRT-code) | [i] | ||
| 26 | No linear OOA(2160, 144, F2, 2, 93) (dual of [(144, 2), 128, 94]-NRT-code) | [i] | ||
| 27 | No linear OOA(2161, 144, F2, 2, 94) (dual of [(144, 2), 127, 95]-NRT-code) | [i] | ||
| 28 | No linear OOA(2162, 144, F2, 2, 95) (dual of [(144, 2), 126, 96]-NRT-code) | [i] | ||
| 29 | No linear OOA(2163, 144, F2, 2, 96) (dual of [(144, 2), 125, 97]-NRT-code) | [i] | ||
| 30 | No linear OOA(2164, 144, F2, 2, 97) (dual of [(144, 2), 124, 98]-NRT-code) | [i] | ||
| 31 | No linear OOA(2165, 144, F2, 2, 98) (dual of [(144, 2), 123, 99]-NRT-code) | [i] | ||
| 32 | No linear OOA(2166, 144, F2, 2, 99) (dual of [(144, 2), 122, 100]-NRT-code) | [i] | ||
| 33 | No linear OOA(2167, 144, F2, 2, 100) (dual of [(144, 2), 121, 101]-NRT-code) | [i] | ||
| 34 | No linear OOA(2168, 144, F2, 2, 101) (dual of [(144, 2), 120, 102]-NRT-code) | [i] | ||
| 35 | No linear OOA(2169, 144, F2, 2, 102) (dual of [(144, 2), 119, 103]-NRT-code) | [i] | ||
| 36 | No linear OOA(2170, 144, F2, 2, 103) (dual of [(144, 2), 118, 104]-NRT-code) | [i] | ||
| 37 | No linear OOA(2171, 144, F2, 2, 104) (dual of [(144, 2), 117, 105]-NRT-code) | [i] | ||
| 38 | No linear OOA(2172, 144, F2, 2, 105) (dual of [(144, 2), 116, 106]-NRT-code) | [i] | ||
| 39 | No linear OOA(2173, 144, F2, 2, 106) (dual of [(144, 2), 115, 107]-NRT-code) | [i] | ||
| 40 | No linear OOA(2174, 144, F2, 2, 107) (dual of [(144, 2), 114, 108]-NRT-code) | [i] | ||
| 41 | No linear OOA(2175, 144, F2, 2, 108) (dual of [(144, 2), 113, 109]-NRT-code) | [i] | ||
| 42 | No linear OOA(2176, 144, F2, 2, 109) (dual of [(144, 2), 112, 110]-NRT-code) | [i] | ||
| 43 | No linear OOA(2177, 144, F2, 2, 110) (dual of [(144, 2), 111, 111]-NRT-code) | [i] | ||
| 44 | No linear OOA(2178, 144, F2, 2, 111) (dual of [(144, 2), 110, 112]-NRT-code) | [i] | ||
| 45 | No linear OOA(2179, 144, F2, 2, 112) (dual of [(144, 2), 109, 113]-NRT-code) | [i] | ||
| 46 | No linear OOA(2180, 144, F2, 2, 113) (dual of [(144, 2), 108, 114]-NRT-code) | [i] | ||
| 47 | No linear OOA(2181, 144, F2, 2, 114) (dual of [(144, 2), 107, 115]-NRT-code) | [i] | ||
| 48 | No linear OOA(2182, 144, F2, 2, 115) (dual of [(144, 2), 106, 116]-NRT-code) | [i] | ||
| 49 | No linear OOA(2183, 144, F2, 2, 116) (dual of [(144, 2), 105, 117]-NRT-code) | [i] | ||
| 50 | No linear OOA(2184, 144, F2, 2, 117) (dual of [(144, 2), 104, 118]-NRT-code) | [i] | ||
| 51 | No linear OOA(2185, 144, F2, 2, 118) (dual of [(144, 2), 103, 119]-NRT-code) | [i] | ||
| 52 | No linear OOA(2186, 144, F2, 2, 119) (dual of [(144, 2), 102, 120]-NRT-code) | [i] | ||
| 53 | No linear OOA(2187, 144, F2, 2, 120) (dual of [(144, 2), 101, 121]-NRT-code) | [i] | ||
| 54 | No linear OOA(2188, 144, F2, 2, 121) (dual of [(144, 2), 100, 122]-NRT-code) | [i] | ||
| 55 | No linear OOA(2189, 144, F2, 2, 122) (dual of [(144, 2), 99, 123]-NRT-code) | [i] | ||
| 56 | No linear OOA(2190, 144, F2, 2, 123) (dual of [(144, 2), 98, 124]-NRT-code) | [i] | ||
| 57 | No linear OOA(2135, 144, F2, 2, 68) (dual of [(144, 2), 153, 69]-NRT-code) | [i] | Depth Reduction | |
| 58 | No linear OOA(2135, 144, F2, 3, 68) (dual of [(144, 3), 297, 69]-NRT-code) | [i] | ||
| 59 | No linear OOA(2135, 144, F2, 4, 68) (dual of [(144, 4), 441, 69]-NRT-code) | [i] | ||
| 60 | No linear OOA(2135, 144, F2, 5, 68) (dual of [(144, 5), 585, 69]-NRT-code) | [i] | ||
| 61 | No linear OOA(2135, 144, F2, 6, 68) (dual of [(144, 6), 729, 69]-NRT-code) | [i] | ||
| 62 | No linear OOA(2135, 144, F2, 7, 68) (dual of [(144, 7), 873, 69]-NRT-code) | [i] | ||
| 63 | No linear OOA(2135, 144, F2, 8, 68) (dual of [(144, 8), 1017, 69]-NRT-code) | [i] | ||
| 64 | No digital (67, 135, 144)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |