Information on Result #548315
There is no linear OA(2118, 127, F2, 60) (dual of [127, 9, 61]-code), because residual code would yield linear OA(258, 66, F2, 30) (dual of [66, 8, 31]-code), but
- adding a parity check bit [i] would yield linear OA(259, 67, F2, 31) (dual of [67, 8, 32]-code), but
- “DHM†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(2119, 128, F2, 61) (dual of [128, 9, 62]-code) | [i] | Truncation | |
| 2 | No linear OA(2120, 129, F2, 62) (dual of [129, 9, 63]-code) | [i] | ||
| 3 | No linear OA(2121, 130, F2, 63) (dual of [130, 9, 64]-code) | [i] | ||
| 4 | No linear OOA(2119, 127, F2, 2, 61) (dual of [(127, 2), 135, 62]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(2120, 127, F2, 2, 62) (dual of [(127, 2), 134, 63]-NRT-code) | [i] | ||
| 6 | No linear OOA(2121, 127, F2, 2, 63) (dual of [(127, 2), 133, 64]-NRT-code) | [i] | ||
| 7 | No linear OOA(2123, 127, F2, 2, 65) (dual of [(127, 2), 131, 66]-NRT-code) | [i] | ||
| 8 | No linear OOA(2124, 127, F2, 2, 66) (dual of [(127, 2), 130, 67]-NRT-code) | [i] | ||
| 9 | No linear OOA(2125, 127, F2, 2, 67) (dual of [(127, 2), 129, 68]-NRT-code) | [i] | ||
| 10 | No linear OOA(2126, 127, F2, 2, 68) (dual of [(127, 2), 128, 69]-NRT-code) | [i] | ||
| 11 | No linear OOA(2127, 127, F2, 2, 69) (dual of [(127, 2), 127, 70]-NRT-code) | [i] | ||
| 12 | No linear OOA(2128, 127, F2, 2, 70) (dual of [(127, 2), 126, 71]-NRT-code) | [i] | ||
| 13 | No linear OOA(2129, 127, F2, 2, 71) (dual of [(127, 2), 125, 72]-NRT-code) | [i] | ||
| 14 | No linear OOA(2130, 127, F2, 2, 72) (dual of [(127, 2), 124, 73]-NRT-code) | [i] | ||
| 15 | No linear OOA(2131, 127, F2, 2, 73) (dual of [(127, 2), 123, 74]-NRT-code) | [i] | ||
| 16 | No linear OOA(2132, 127, F2, 2, 74) (dual of [(127, 2), 122, 75]-NRT-code) | [i] | ||
| 17 | No linear OOA(2133, 127, F2, 2, 75) (dual of [(127, 2), 121, 76]-NRT-code) | [i] | ||
| 18 | No linear OOA(2134, 127, F2, 2, 76) (dual of [(127, 2), 120, 77]-NRT-code) | [i] | ||
| 19 | No linear OOA(2135, 127, F2, 2, 77) (dual of [(127, 2), 119, 78]-NRT-code) | [i] | ||
| 20 | No linear OOA(2136, 127, F2, 2, 78) (dual of [(127, 2), 118, 79]-NRT-code) | [i] | ||
| 21 | No linear OOA(2137, 127, F2, 2, 79) (dual of [(127, 2), 117, 80]-NRT-code) | [i] | ||
| 22 | No linear OOA(2138, 127, F2, 2, 80) (dual of [(127, 2), 116, 81]-NRT-code) | [i] | ||
| 23 | No linear OOA(2139, 127, F2, 2, 81) (dual of [(127, 2), 115, 82]-NRT-code) | [i] | ||
| 24 | No linear OOA(2140, 127, F2, 2, 82) (dual of [(127, 2), 114, 83]-NRT-code) | [i] | ||
| 25 | No linear OOA(2141, 127, F2, 2, 83) (dual of [(127, 2), 113, 84]-NRT-code) | [i] | ||
| 26 | No linear OOA(2142, 127, F2, 2, 84) (dual of [(127, 2), 112, 85]-NRT-code) | [i] | ||
| 27 | No linear OOA(2143, 127, F2, 2, 85) (dual of [(127, 2), 111, 86]-NRT-code) | [i] | ||
| 28 | No linear OOA(2144, 127, F2, 2, 86) (dual of [(127, 2), 110, 87]-NRT-code) | [i] | ||
| 29 | No linear OOA(2145, 127, F2, 2, 87) (dual of [(127, 2), 109, 88]-NRT-code) | [i] | ||
| 30 | No linear OOA(2146, 127, F2, 2, 88) (dual of [(127, 2), 108, 89]-NRT-code) | [i] | ||
| 31 | No linear OOA(2147, 127, F2, 2, 89) (dual of [(127, 2), 107, 90]-NRT-code) | [i] | ||
| 32 | No linear OOA(2148, 127, F2, 2, 90) (dual of [(127, 2), 106, 91]-NRT-code) | [i] | ||
| 33 | No linear OOA(2149, 127, F2, 2, 91) (dual of [(127, 2), 105, 92]-NRT-code) | [i] | ||
| 34 | No linear OOA(2150, 127, F2, 2, 92) (dual of [(127, 2), 104, 93]-NRT-code) | [i] | ||
| 35 | No linear OOA(2151, 127, F2, 2, 93) (dual of [(127, 2), 103, 94]-NRT-code) | [i] | ||
| 36 | No linear OOA(2152, 127, F2, 2, 94) (dual of [(127, 2), 102, 95]-NRT-code) | [i] | ||
| 37 | No linear OOA(2153, 127, F2, 2, 95) (dual of [(127, 2), 101, 96]-NRT-code) | [i] | ||
| 38 | No linear OOA(2154, 127, F2, 2, 96) (dual of [(127, 2), 100, 97]-NRT-code) | [i] | ||
| 39 | No linear OOA(2155, 127, F2, 2, 97) (dual of [(127, 2), 99, 98]-NRT-code) | [i] | ||
| 40 | No linear OOA(2156, 127, F2, 2, 98) (dual of [(127, 2), 98, 99]-NRT-code) | [i] | ||
| 41 | No linear OOA(2157, 127, F2, 2, 99) (dual of [(127, 2), 97, 100]-NRT-code) | [i] | ||
| 42 | No linear OOA(2158, 127, F2, 2, 100) (dual of [(127, 2), 96, 101]-NRT-code) | [i] | ||
| 43 | No linear OOA(2159, 127, F2, 2, 101) (dual of [(127, 2), 95, 102]-NRT-code) | [i] | ||
| 44 | No linear OOA(2160, 127, F2, 2, 102) (dual of [(127, 2), 94, 103]-NRT-code) | [i] | ||
| 45 | No linear OOA(2161, 127, F2, 2, 103) (dual of [(127, 2), 93, 104]-NRT-code) | [i] | ||
| 46 | No linear OOA(2162, 127, F2, 2, 104) (dual of [(127, 2), 92, 105]-NRT-code) | [i] | ||
| 47 | No linear OOA(2163, 127, F2, 2, 105) (dual of [(127, 2), 91, 106]-NRT-code) | [i] | ||
| 48 | No linear OOA(2164, 127, F2, 2, 106) (dual of [(127, 2), 90, 107]-NRT-code) | [i] | ||
| 49 | No linear OOA(2165, 127, F2, 2, 107) (dual of [(127, 2), 89, 108]-NRT-code) | [i] | ||
| 50 | No linear OOA(2166, 127, F2, 2, 108) (dual of [(127, 2), 88, 109]-NRT-code) | [i] | ||
| 51 | No linear OOA(2118, 127, F2, 2, 60) (dual of [(127, 2), 136, 61]-NRT-code) | [i] | Depth Reduction | |
| 52 | No linear OOA(2118, 127, F2, 3, 60) (dual of [(127, 3), 263, 61]-NRT-code) | [i] | ||
| 53 | No linear OOA(2118, 127, F2, 4, 60) (dual of [(127, 4), 390, 61]-NRT-code) | [i] | ||
| 54 | No linear OOA(2118, 127, F2, 5, 60) (dual of [(127, 5), 517, 61]-NRT-code) | [i] | ||
| 55 | No linear OOA(2118, 127, F2, 6, 60) (dual of [(127, 6), 644, 61]-NRT-code) | [i] | ||
| 56 | No linear OOA(2118, 127, F2, 7, 60) (dual of [(127, 7), 771, 61]-NRT-code) | [i] | ||
| 57 | No linear OOA(2118, 127, F2, 8, 60) (dual of [(127, 8), 898, 61]-NRT-code) | [i] | ||
| 58 | No digital (58, 118, 127)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 59 | No linear OA(2238, 248, F2, 120) (dual of [248, 10, 121]-code) | [i] | Residual Code | |