Information on Result #548319
There is no linear OA(2128, 137, F2, 64) (dual of [137, 9, 65]-code), because residual code would yield linear OA(264, 72, F2, 32) (dual of [72, 8, 33]-code), but
- adding a parity check bit [i] would yield linear OA(265, 73, F2, 33) (dual of [73, 8, 34]-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(2129, 138, F2, 65) (dual of [138, 9, 66]-code) | [i] | Truncation | |
| 2 | No linear OA(2131, 140, F2, 67) (dual of [140, 9, 68]-code) | [i] | ||
| 3 | No linear OOA(2129, 137, F2, 2, 65) (dual of [(137, 2), 145, 66]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(2130, 137, F2, 2, 66) (dual of [(137, 2), 144, 67]-NRT-code) | [i] | ||
| 5 | No linear OOA(2131, 137, F2, 2, 67) (dual of [(137, 2), 143, 68]-NRT-code) | [i] | ||
| 6 | No linear OOA(2132, 137, F2, 2, 68) (dual of [(137, 2), 142, 69]-NRT-code) | [i] | ||
| 7 | No linear OOA(2133, 137, F2, 2, 69) (dual of [(137, 2), 141, 70]-NRT-code) | [i] | ||
| 8 | No linear OOA(2134, 137, F2, 2, 70) (dual of [(137, 2), 140, 71]-NRT-code) | [i] | ||
| 9 | No linear OOA(2135, 137, F2, 2, 71) (dual of [(137, 2), 139, 72]-NRT-code) | [i] | ||
| 10 | No linear OOA(2136, 137, F2, 2, 72) (dual of [(137, 2), 138, 73]-NRT-code) | [i] | ||
| 11 | No linear OOA(2137, 137, F2, 2, 73) (dual of [(137, 2), 137, 74]-NRT-code) | [i] | ||
| 12 | No linear OOA(2138, 137, F2, 2, 74) (dual of [(137, 2), 136, 75]-NRT-code) | [i] | ||
| 13 | No linear OOA(2139, 137, F2, 2, 75) (dual of [(137, 2), 135, 76]-NRT-code) | [i] | ||
| 14 | No linear OOA(2140, 137, F2, 2, 76) (dual of [(137, 2), 134, 77]-NRT-code) | [i] | ||
| 15 | No linear OOA(2141, 137, F2, 2, 77) (dual of [(137, 2), 133, 78]-NRT-code) | [i] | ||
| 16 | No linear OOA(2142, 137, F2, 2, 78) (dual of [(137, 2), 132, 79]-NRT-code) | [i] | ||
| 17 | No linear OOA(2143, 137, F2, 2, 79) (dual of [(137, 2), 131, 80]-NRT-code) | [i] | ||
| 18 | No linear OOA(2144, 137, F2, 2, 80) (dual of [(137, 2), 130, 81]-NRT-code) | [i] | ||
| 19 | No linear OOA(2145, 137, F2, 2, 81) (dual of [(137, 2), 129, 82]-NRT-code) | [i] | ||
| 20 | No linear OOA(2146, 137, F2, 2, 82) (dual of [(137, 2), 128, 83]-NRT-code) | [i] | ||
| 21 | No linear OOA(2147, 137, F2, 2, 83) (dual of [(137, 2), 127, 84]-NRT-code) | [i] | ||
| 22 | No linear OOA(2148, 137, F2, 2, 84) (dual of [(137, 2), 126, 85]-NRT-code) | [i] | ||
| 23 | No linear OOA(2149, 137, F2, 2, 85) (dual of [(137, 2), 125, 86]-NRT-code) | [i] | ||
| 24 | No linear OOA(2150, 137, F2, 2, 86) (dual of [(137, 2), 124, 87]-NRT-code) | [i] | ||
| 25 | No linear OOA(2151, 137, F2, 2, 87) (dual of [(137, 2), 123, 88]-NRT-code) | [i] | ||
| 26 | No linear OOA(2152, 137, F2, 2, 88) (dual of [(137, 2), 122, 89]-NRT-code) | [i] | ||
| 27 | No linear OOA(2153, 137, F2, 2, 89) (dual of [(137, 2), 121, 90]-NRT-code) | [i] | ||
| 28 | No linear OOA(2154, 137, F2, 2, 90) (dual of [(137, 2), 120, 91]-NRT-code) | [i] | ||
| 29 | No linear OOA(2155, 137, F2, 2, 91) (dual of [(137, 2), 119, 92]-NRT-code) | [i] | ||
| 30 | No linear OOA(2156, 137, F2, 2, 92) (dual of [(137, 2), 118, 93]-NRT-code) | [i] | ||
| 31 | No linear OOA(2157, 137, F2, 2, 93) (dual of [(137, 2), 117, 94]-NRT-code) | [i] | ||
| 32 | No linear OOA(2158, 137, F2, 2, 94) (dual of [(137, 2), 116, 95]-NRT-code) | [i] | ||
| 33 | No linear OOA(2159, 137, F2, 2, 95) (dual of [(137, 2), 115, 96]-NRT-code) | [i] | ||
| 34 | No linear OOA(2160, 137, F2, 2, 96) (dual of [(137, 2), 114, 97]-NRT-code) | [i] | ||
| 35 | No linear OOA(2161, 137, F2, 2, 97) (dual of [(137, 2), 113, 98]-NRT-code) | [i] | ||
| 36 | No linear OOA(2162, 137, F2, 2, 98) (dual of [(137, 2), 112, 99]-NRT-code) | [i] | ||
| 37 | No linear OOA(2163, 137, F2, 2, 99) (dual of [(137, 2), 111, 100]-NRT-code) | [i] | ||
| 38 | No linear OOA(2164, 137, F2, 2, 100) (dual of [(137, 2), 110, 101]-NRT-code) | [i] | ||
| 39 | No linear OOA(2165, 137, F2, 2, 101) (dual of [(137, 2), 109, 102]-NRT-code) | [i] | ||
| 40 | No linear OOA(2166, 137, F2, 2, 102) (dual of [(137, 2), 108, 103]-NRT-code) | [i] | ||
| 41 | No linear OOA(2167, 137, F2, 2, 103) (dual of [(137, 2), 107, 104]-NRT-code) | [i] | ||
| 42 | No linear OOA(2168, 137, F2, 2, 104) (dual of [(137, 2), 106, 105]-NRT-code) | [i] | ||
| 43 | No linear OOA(2169, 137, F2, 2, 105) (dual of [(137, 2), 105, 106]-NRT-code) | [i] | ||
| 44 | No linear OOA(2170, 137, F2, 2, 106) (dual of [(137, 2), 104, 107]-NRT-code) | [i] | ||
| 45 | No linear OOA(2171, 137, F2, 2, 107) (dual of [(137, 2), 103, 108]-NRT-code) | [i] | ||
| 46 | No linear OOA(2172, 137, F2, 2, 108) (dual of [(137, 2), 102, 109]-NRT-code) | [i] | ||
| 47 | No linear OOA(2173, 137, F2, 2, 109) (dual of [(137, 2), 101, 110]-NRT-code) | [i] | ||
| 48 | No linear OOA(2174, 137, F2, 2, 110) (dual of [(137, 2), 100, 111]-NRT-code) | [i] | ||
| 49 | No linear OOA(2175, 137, F2, 2, 111) (dual of [(137, 2), 99, 112]-NRT-code) | [i] | ||
| 50 | No linear OOA(2176, 137, F2, 2, 112) (dual of [(137, 2), 98, 113]-NRT-code) | [i] | ||
| 51 | No linear OOA(2177, 137, F2, 2, 113) (dual of [(137, 2), 97, 114]-NRT-code) | [i] | ||
| 52 | No linear OOA(2178, 137, F2, 2, 114) (dual of [(137, 2), 96, 115]-NRT-code) | [i] | ||
| 53 | No linear OOA(2179, 137, F2, 2, 115) (dual of [(137, 2), 95, 116]-NRT-code) | [i] | ||
| 54 | No linear OOA(2180, 137, F2, 2, 116) (dual of [(137, 2), 94, 117]-NRT-code) | [i] | ||
| 55 | No linear OOA(2181, 137, F2, 2, 117) (dual of [(137, 2), 93, 118]-NRT-code) | [i] | ||
| 56 | No linear OOA(2182, 137, F2, 2, 118) (dual of [(137, 2), 92, 119]-NRT-code) | [i] | ||
| 57 | No linear OOA(2128, 137, F2, 2, 64) (dual of [(137, 2), 146, 65]-NRT-code) | [i] | Depth Reduction | |
| 58 | No linear OOA(2128, 137, F2, 3, 64) (dual of [(137, 3), 283, 65]-NRT-code) | [i] | ||
| 59 | No linear OOA(2128, 137, F2, 4, 64) (dual of [(137, 4), 420, 65]-NRT-code) | [i] | ||
| 60 | No linear OOA(2128, 137, F2, 5, 64) (dual of [(137, 5), 557, 65]-NRT-code) | [i] | ||
| 61 | No linear OOA(2128, 137, F2, 6, 64) (dual of [(137, 6), 694, 65]-NRT-code) | [i] | ||
| 62 | No linear OOA(2128, 137, F2, 7, 64) (dual of [(137, 7), 831, 65]-NRT-code) | [i] | ||
| 63 | No linear OOA(2128, 137, F2, 8, 64) (dual of [(137, 8), 968, 65]-NRT-code) | [i] | ||
| 64 | No digital (64, 128, 137)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 65 | No linear OA(2256, 266, F2, 128) (dual of [266, 10, 129]-code) | [i] | Residual Code | |
| 66 | No linear OA(2129, 141, F2, 64) (dual of [141, 12, 65]-code) | [i] | Construction Y1 (Bound) | |