Information on Result #548299
There is no linear OA(294, 102, F2, 48) (dual of [102, 8, 49]-code), because residual code would yield linear OA(246, 53, F2, 24) (dual of [53, 7, 25]-code), but
- 1 times code embedding in larger space [i] would yield linear OA(247, 54, F2, 24) (dual of [54, 7, 25]-code), but
- adding a parity check bit [i] would yield linear OA(248, 55, F2, 25) (dual of [55, 7, 26]-code), but
- “vT4†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(248, 55, F2, 25) (dual of [55, 7, 26]-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(295, 103, F2, 49) (dual of [103, 8, 50]-code) | [i] | Truncation | |
| 2 | No linear OOA(295, 102, F2, 2, 49) (dual of [(102, 2), 109, 50]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(297, 102, F2, 2, 51) (dual of [(102, 2), 107, 52]-NRT-code) | [i] | ||
| 4 | No linear OOA(298, 102, F2, 2, 52) (dual of [(102, 2), 106, 53]-NRT-code) | [i] | ||
| 5 | No linear OOA(299, 102, F2, 2, 53) (dual of [(102, 2), 105, 54]-NRT-code) | [i] | ||
| 6 | No linear OOA(2100, 102, F2, 2, 54) (dual of [(102, 2), 104, 55]-NRT-code) | [i] | ||
| 7 | No linear OOA(2101, 102, F2, 2, 55) (dual of [(102, 2), 103, 56]-NRT-code) | [i] | ||
| 8 | No linear OOA(2102, 102, F2, 2, 56) (dual of [(102, 2), 102, 57]-NRT-code) | [i] | ||
| 9 | No linear OOA(2103, 102, F2, 2, 57) (dual of [(102, 2), 101, 58]-NRT-code) | [i] | ||
| 10 | No linear OOA(2104, 102, F2, 2, 58) (dual of [(102, 2), 100, 59]-NRT-code) | [i] | ||
| 11 | No linear OOA(2105, 102, F2, 2, 59) (dual of [(102, 2), 99, 60]-NRT-code) | [i] | ||
| 12 | No linear OOA(2106, 102, F2, 2, 60) (dual of [(102, 2), 98, 61]-NRT-code) | [i] | ||
| 13 | No linear OOA(2107, 102, F2, 2, 61) (dual of [(102, 2), 97, 62]-NRT-code) | [i] | ||
| 14 | No linear OOA(2108, 102, F2, 2, 62) (dual of [(102, 2), 96, 63]-NRT-code) | [i] | ||
| 15 | No linear OOA(2109, 102, F2, 2, 63) (dual of [(102, 2), 95, 64]-NRT-code) | [i] | ||
| 16 | No linear OOA(2110, 102, F2, 2, 64) (dual of [(102, 2), 94, 65]-NRT-code) | [i] | ||
| 17 | No linear OOA(2111, 102, F2, 2, 65) (dual of [(102, 2), 93, 66]-NRT-code) | [i] | ||
| 18 | No linear OOA(2112, 102, F2, 2, 66) (dual of [(102, 2), 92, 67]-NRT-code) | [i] | ||
| 19 | No linear OOA(2113, 102, F2, 2, 67) (dual of [(102, 2), 91, 68]-NRT-code) | [i] | ||
| 20 | No linear OOA(2114, 102, F2, 2, 68) (dual of [(102, 2), 90, 69]-NRT-code) | [i] | ||
| 21 | No linear OOA(2115, 102, F2, 2, 69) (dual of [(102, 2), 89, 70]-NRT-code) | [i] | ||
| 22 | No linear OOA(2116, 102, F2, 2, 70) (dual of [(102, 2), 88, 71]-NRT-code) | [i] | ||
| 23 | No linear OOA(2117, 102, F2, 2, 71) (dual of [(102, 2), 87, 72]-NRT-code) | [i] | ||
| 24 | No linear OOA(2118, 102, F2, 2, 72) (dual of [(102, 2), 86, 73]-NRT-code) | [i] | ||
| 25 | No linear OOA(2119, 102, F2, 2, 73) (dual of [(102, 2), 85, 74]-NRT-code) | [i] | ||
| 26 | No linear OOA(2120, 102, F2, 2, 74) (dual of [(102, 2), 84, 75]-NRT-code) | [i] | ||
| 27 | No linear OOA(2121, 102, F2, 2, 75) (dual of [(102, 2), 83, 76]-NRT-code) | [i] | ||
| 28 | No linear OOA(2122, 102, F2, 2, 76) (dual of [(102, 2), 82, 77]-NRT-code) | [i] | ||
| 29 | No linear OOA(2123, 102, F2, 2, 77) (dual of [(102, 2), 81, 78]-NRT-code) | [i] | ||
| 30 | No linear OOA(2124, 102, F2, 2, 78) (dual of [(102, 2), 80, 79]-NRT-code) | [i] | ||
| 31 | No linear OOA(2125, 102, F2, 2, 79) (dual of [(102, 2), 79, 80]-NRT-code) | [i] | ||
| 32 | No linear OOA(2126, 102, F2, 2, 80) (dual of [(102, 2), 78, 81]-NRT-code) | [i] | ||
| 33 | No linear OOA(2127, 102, F2, 2, 81) (dual of [(102, 2), 77, 82]-NRT-code) | [i] | ||
| 34 | No linear OOA(2128, 102, F2, 2, 82) (dual of [(102, 2), 76, 83]-NRT-code) | [i] | ||
| 35 | No linear OOA(2129, 102, F2, 2, 83) (dual of [(102, 2), 75, 84]-NRT-code) | [i] | ||
| 36 | No linear OOA(2130, 102, F2, 2, 84) (dual of [(102, 2), 74, 85]-NRT-code) | [i] | ||
| 37 | No linear OOA(2131, 102, F2, 2, 85) (dual of [(102, 2), 73, 86]-NRT-code) | [i] | ||
| 38 | No linear OOA(2132, 102, F2, 2, 86) (dual of [(102, 2), 72, 87]-NRT-code) | [i] | ||
| 39 | No linear OOA(2133, 102, F2, 2, 87) (dual of [(102, 2), 71, 88]-NRT-code) | [i] | ||
| 40 | No linear OOA(294, 102, F2, 2, 48) (dual of [(102, 2), 110, 49]-NRT-code) | [i] | Depth Reduction | |
| 41 | No linear OOA(294, 102, F2, 3, 48) (dual of [(102, 3), 212, 49]-NRT-code) | [i] | ||
| 42 | No linear OOA(294, 102, F2, 4, 48) (dual of [(102, 4), 314, 49]-NRT-code) | [i] | ||
| 43 | No linear OOA(294, 102, F2, 5, 48) (dual of [(102, 5), 416, 49]-NRT-code) | [i] | ||
| 44 | No linear OOA(294, 102, F2, 6, 48) (dual of [(102, 6), 518, 49]-NRT-code) | [i] | ||
| 45 | No linear OOA(294, 102, F2, 7, 48) (dual of [(102, 7), 620, 49]-NRT-code) | [i] | ||
| 46 | No linear OOA(294, 102, F2, 8, 48) (dual of [(102, 8), 722, 49]-NRT-code) | [i] | ||
| 47 | No digital (46, 94, 102)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 48 | No linear OA(2190, 199, F2, 96) (dual of [199, 9, 97]-code) | [i] | Residual Code | |