Information on Result #546168
There is no linear OA(263, 71, F2, 32) (dual of [71, 8, 33]-code), because residual code would yield linear OA(231, 38, F2, 16) (dual of [38, 7, 17]-code), but
- residual code [i] would yield linear OA(215, 21, F2, 8) (dual of [21, 6, 9]-code), but
- residual code [i] would yield linear OA(27, 12, F2, 4) (dual of [12, 5, 5]-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(264, 72, F2, 33) (dual of [72, 8, 34]-code) | [i] | Truncation | |
| 2 | No linear OOA(264, 71, F2, 2, 33) (dual of [(71, 2), 78, 34]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(266, 71, F2, 2, 35) (dual of [(71, 2), 76, 36]-NRT-code) | [i] | ||
| 4 | No linear OOA(267, 71, F2, 2, 36) (dual of [(71, 2), 75, 37]-NRT-code) | [i] | ||
| 5 | No linear OOA(268, 71, F2, 2, 37) (dual of [(71, 2), 74, 38]-NRT-code) | [i] | ||
| 6 | No linear OOA(269, 71, F2, 2, 38) (dual of [(71, 2), 73, 39]-NRT-code) | [i] | ||
| 7 | No linear OOA(270, 71, F2, 2, 39) (dual of [(71, 2), 72, 40]-NRT-code) | [i] | ||
| 8 | No linear OOA(271, 71, F2, 2, 40) (dual of [(71, 2), 71, 41]-NRT-code) | [i] | ||
| 9 | No linear OOA(272, 71, F2, 2, 41) (dual of [(71, 2), 70, 42]-NRT-code) | [i] | ||
| 10 | No linear OOA(273, 71, F2, 2, 42) (dual of [(71, 2), 69, 43]-NRT-code) | [i] | ||
| 11 | No linear OOA(274, 71, F2, 2, 43) (dual of [(71, 2), 68, 44]-NRT-code) | [i] | ||
| 12 | No linear OOA(275, 71, F2, 2, 44) (dual of [(71, 2), 67, 45]-NRT-code) | [i] | ||
| 13 | No linear OOA(276, 71, F2, 2, 45) (dual of [(71, 2), 66, 46]-NRT-code) | [i] | ||
| 14 | No linear OOA(277, 71, F2, 2, 46) (dual of [(71, 2), 65, 47]-NRT-code) | [i] | ||
| 15 | No linear OOA(278, 71, F2, 2, 47) (dual of [(71, 2), 64, 48]-NRT-code) | [i] | ||
| 16 | No linear OOA(279, 71, F2, 2, 48) (dual of [(71, 2), 63, 49]-NRT-code) | [i] | ||
| 17 | No linear OOA(280, 71, F2, 2, 49) (dual of [(71, 2), 62, 50]-NRT-code) | [i] | ||
| 18 | No linear OOA(281, 71, F2, 2, 50) (dual of [(71, 2), 61, 51]-NRT-code) | [i] | ||
| 19 | No linear OOA(282, 71, F2, 2, 51) (dual of [(71, 2), 60, 52]-NRT-code) | [i] | ||
| 20 | No linear OOA(283, 71, F2, 2, 52) (dual of [(71, 2), 59, 53]-NRT-code) | [i] | ||
| 21 | No linear OOA(284, 71, F2, 2, 53) (dual of [(71, 2), 58, 54]-NRT-code) | [i] | ||
| 22 | No linear OOA(285, 71, F2, 2, 54) (dual of [(71, 2), 57, 55]-NRT-code) | [i] | ||
| 23 | No linear OOA(286, 71, F2, 2, 55) (dual of [(71, 2), 56, 56]-NRT-code) | [i] | ||
| 24 | No linear OOA(287, 71, F2, 2, 56) (dual of [(71, 2), 55, 57]-NRT-code) | [i] | ||
| 25 | No linear OOA(288, 71, F2, 2, 57) (dual of [(71, 2), 54, 58]-NRT-code) | [i] | ||
| 26 | No linear OOA(289, 71, F2, 2, 58) (dual of [(71, 2), 53, 59]-NRT-code) | [i] | ||
| 27 | No linear OOA(290, 71, F2, 2, 59) (dual of [(71, 2), 52, 60]-NRT-code) | [i] | ||
| 28 | No linear OOA(291, 71, F2, 2, 60) (dual of [(71, 2), 51, 61]-NRT-code) | [i] | ||
| 29 | No linear OOA(292, 71, F2, 2, 61) (dual of [(71, 2), 50, 62]-NRT-code) | [i] | ||
| 30 | No linear OOA(263, 71, F2, 2, 32) (dual of [(71, 2), 79, 33]-NRT-code) | [i] | Depth Reduction | |
| 31 | No linear OOA(263, 71, F2, 3, 32) (dual of [(71, 3), 150, 33]-NRT-code) | [i] | ||
| 32 | No linear OOA(263, 71, F2, 4, 32) (dual of [(71, 4), 221, 33]-NRT-code) | [i] | ||
| 33 | No linear OOA(263, 71, F2, 5, 32) (dual of [(71, 5), 292, 33]-NRT-code) | [i] | ||
| 34 | No linear OOA(263, 71, F2, 6, 32) (dual of [(71, 6), 363, 33]-NRT-code) | [i] | ||
| 35 | No linear OOA(263, 71, F2, 7, 32) (dual of [(71, 7), 434, 33]-NRT-code) | [i] | ||
| 36 | No linear OOA(263, 71, F2, 8, 32) (dual of [(71, 8), 505, 33]-NRT-code) | [i] | ||
| 37 | No digital (31, 63, 71)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |
| 38 | No linear OA(2127, 136, F2, 64) (dual of [136, 9, 65]-code) | [i] | Residual Code | |
| 39 | No linear OA(264, 75, F2, 32) (dual of [75, 11, 33]-code) | [i] | Construction Y1 (Bound) | |