Information on Result #548311
There is no linear OA(2112, 123, F2, 56) (dual of [123, 11, 57]-code), because residual code 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(2113, 124, F2, 57) (dual of [124, 11, 58]-code) | [i] | Truncation | |
| 2 | No linear OOA(2113, 123, F2, 2, 57) (dual of [(123, 2), 133, 58]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2115, 123, F2, 2, 59) (dual of [(123, 2), 131, 60]-NRT-code) | [i] | ||
| 4 | No linear OOA(2116, 123, F2, 2, 60) (dual of [(123, 2), 130, 61]-NRT-code) | [i] | ||
| 5 | No linear OOA(2117, 123, F2, 2, 61) (dual of [(123, 2), 129, 62]-NRT-code) | [i] | ||
| 6 | No linear OOA(2118, 123, F2, 2, 62) (dual of [(123, 2), 128, 63]-NRT-code) | [i] | ||
| 7 | No linear OOA(2119, 123, F2, 2, 63) (dual of [(123, 2), 127, 64]-NRT-code) | [i] | ||
| 8 | No linear OOA(2120, 123, F2, 2, 64) (dual of [(123, 2), 126, 65]-NRT-code) | [i] | ||
| 9 | No linear OOA(2121, 123, F2, 2, 65) (dual of [(123, 2), 125, 66]-NRT-code) | [i] | ||
| 10 | No linear OOA(2122, 123, F2, 2, 66) (dual of [(123, 2), 124, 67]-NRT-code) | [i] | ||
| 11 | No linear OOA(2123, 123, F2, 2, 67) (dual of [(123, 2), 123, 68]-NRT-code) | [i] | ||
| 12 | No linear OOA(2124, 123, F2, 2, 68) (dual of [(123, 2), 122, 69]-NRT-code) | [i] | ||
| 13 | No linear OOA(2125, 123, F2, 2, 69) (dual of [(123, 2), 121, 70]-NRT-code) | [i] | ||
| 14 | No linear OOA(2126, 123, F2, 2, 70) (dual of [(123, 2), 120, 71]-NRT-code) | [i] | ||
| 15 | No linear OOA(2127, 123, F2, 2, 71) (dual of [(123, 2), 119, 72]-NRT-code) | [i] | ||
| 16 | No linear OOA(2128, 123, F2, 2, 72) (dual of [(123, 2), 118, 73]-NRT-code) | [i] | ||
| 17 | No linear OOA(2129, 123, F2, 2, 73) (dual of [(123, 2), 117, 74]-NRT-code) | [i] | ||
| 18 | No linear OOA(2130, 123, F2, 2, 74) (dual of [(123, 2), 116, 75]-NRT-code) | [i] | ||
| 19 | No linear OOA(2131, 123, F2, 2, 75) (dual of [(123, 2), 115, 76]-NRT-code) | [i] | ||
| 20 | No linear OOA(2132, 123, F2, 2, 76) (dual of [(123, 2), 114, 77]-NRT-code) | [i] | ||
| 21 | No linear OOA(2133, 123, F2, 2, 77) (dual of [(123, 2), 113, 78]-NRT-code) | [i] | ||
| 22 | No linear OOA(2134, 123, F2, 2, 78) (dual of [(123, 2), 112, 79]-NRT-code) | [i] | ||
| 23 | No linear OOA(2135, 123, F2, 2, 79) (dual of [(123, 2), 111, 80]-NRT-code) | [i] | ||
| 24 | No linear OOA(2136, 123, F2, 2, 80) (dual of [(123, 2), 110, 81]-NRT-code) | [i] | ||
| 25 | No linear OOA(2137, 123, F2, 2, 81) (dual of [(123, 2), 109, 82]-NRT-code) | [i] | ||
| 26 | No linear OOA(2138, 123, F2, 2, 82) (dual of [(123, 2), 108, 83]-NRT-code) | [i] | ||
| 27 | No linear OOA(2139, 123, F2, 2, 83) (dual of [(123, 2), 107, 84]-NRT-code) | [i] | ||
| 28 | No linear OOA(2140, 123, F2, 2, 84) (dual of [(123, 2), 106, 85]-NRT-code) | [i] | ||
| 29 | No linear OOA(2141, 123, F2, 2, 85) (dual of [(123, 2), 105, 86]-NRT-code) | [i] | ||
| 30 | No linear OOA(2142, 123, F2, 2, 86) (dual of [(123, 2), 104, 87]-NRT-code) | [i] | ||
| 31 | No linear OOA(2143, 123, F2, 2, 87) (dual of [(123, 2), 103, 88]-NRT-code) | [i] | ||
| 32 | No linear OOA(2144, 123, F2, 2, 88) (dual of [(123, 2), 102, 89]-NRT-code) | [i] | ||
| 33 | No linear OOA(2145, 123, F2, 2, 89) (dual of [(123, 2), 101, 90]-NRT-code) | [i] | ||
| 34 | No linear OOA(2146, 123, F2, 2, 90) (dual of [(123, 2), 100, 91]-NRT-code) | [i] | ||
| 35 | No linear OOA(2147, 123, F2, 2, 91) (dual of [(123, 2), 99, 92]-NRT-code) | [i] | ||
| 36 | No linear OOA(2148, 123, F2, 2, 92) (dual of [(123, 2), 98, 93]-NRT-code) | [i] | ||
| 37 | No linear OOA(2149, 123, F2, 2, 93) (dual of [(123, 2), 97, 94]-NRT-code) | [i] | ||
| 38 | No linear OOA(2150, 123, F2, 2, 94) (dual of [(123, 2), 96, 95]-NRT-code) | [i] | ||
| 39 | No linear OOA(2151, 123, F2, 2, 95) (dual of [(123, 2), 95, 96]-NRT-code) | [i] | ||
| 40 | No linear OOA(2152, 123, F2, 2, 96) (dual of [(123, 2), 94, 97]-NRT-code) | [i] | ||
| 41 | No linear OOA(2153, 123, F2, 2, 97) (dual of [(123, 2), 93, 98]-NRT-code) | [i] | ||
| 42 | No linear OOA(2154, 123, F2, 2, 98) (dual of [(123, 2), 92, 99]-NRT-code) | [i] | ||
| 43 | No linear OOA(2155, 123, F2, 2, 99) (dual of [(123, 2), 91, 100]-NRT-code) | [i] | ||
| 44 | No linear OOA(2156, 123, F2, 2, 100) (dual of [(123, 2), 90, 101]-NRT-code) | [i] | ||
| 45 | No linear OOA(2157, 123, F2, 2, 101) (dual of [(123, 2), 89, 102]-NRT-code) | [i] | ||
| 46 | No linear OOA(2158, 123, F2, 2, 102) (dual of [(123, 2), 88, 103]-NRT-code) | [i] | ||
| 47 | No linear OOA(2159, 123, F2, 2, 103) (dual of [(123, 2), 87, 104]-NRT-code) | [i] | ||
| 48 | No linear OOA(2160, 123, F2, 2, 104) (dual of [(123, 2), 86, 105]-NRT-code) | [i] | ||
| 49 | No linear OOA(2112, 123, F2, 2, 56) (dual of [(123, 2), 134, 57]-NRT-code) | [i] | Depth Reduction | |
| 50 | No linear OOA(2112, 123, F2, 3, 56) (dual of [(123, 3), 257, 57]-NRT-code) | [i] | ||
| 51 | No linear OOA(2112, 123, F2, 4, 56) (dual of [(123, 4), 380, 57]-NRT-code) | [i] | ||
| 52 | No linear OOA(2112, 123, F2, 5, 56) (dual of [(123, 5), 503, 57]-NRT-code) | [i] | ||
| 53 | No linear OOA(2112, 123, F2, 6, 56) (dual of [(123, 6), 626, 57]-NRT-code) | [i] | ||
| 54 | No linear OOA(2112, 123, F2, 7, 56) (dual of [(123, 7), 749, 57]-NRT-code) | [i] | ||
| 55 | No linear OOA(2112, 123, F2, 8, 56) (dual of [(123, 8), 872, 57]-NRT-code) | [i] | ||
| 56 | No digital (56, 112, 123)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 57 | No linear OA(2224, 236, F2, 112) (dual of [236, 12, 113]-code) | [i] | Residual Code | |