Information on Result #526678
There is no linear OA(2753, 56, F27, 52) (dual of [56, 3, 53]-code), because bound for almost-MDS-codes with dimension n = 3
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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(2754, 57, F27, 53) (dual of [57, 3, 54]-code) | [i] | Truncation | |
| 2 | No linear OOA(2754, 56, F27, 2, 53) (dual of [(56, 2), 58, 54]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2755, 56, F27, 2, 54) (dual of [(56, 2), 57, 55]-NRT-code) | [i] | ||
| 4 | No linear OOA(2756, 56, F27, 2, 55) (dual of [(56, 2), 56, 56]-NRT-code) | [i] | ||
| 5 | No linear OOA(2757, 56, F27, 2, 56) (dual of [(56, 2), 55, 57]-NRT-code) | [i] | ||
| 6 | No linear OOA(2758, 56, F27, 2, 57) (dual of [(56, 2), 54, 58]-NRT-code) | [i] | ||
| 7 | No linear OOA(2759, 56, F27, 2, 58) (dual of [(56, 2), 53, 59]-NRT-code) | [i] | ||
| 8 | No linear OOA(2760, 56, F27, 2, 59) (dual of [(56, 2), 52, 60]-NRT-code) | [i] | ||
| 9 | No linear OOA(2761, 56, F27, 2, 60) (dual of [(56, 2), 51, 61]-NRT-code) | [i] | ||
| 10 | No linear OOA(2762, 56, F27, 2, 61) (dual of [(56, 2), 50, 62]-NRT-code) | [i] | ||
| 11 | No linear OOA(2763, 56, F27, 2, 62) (dual of [(56, 2), 49, 63]-NRT-code) | [i] | ||
| 12 | No linear OOA(2764, 56, F27, 2, 63) (dual of [(56, 2), 48, 64]-NRT-code) | [i] | ||
| 13 | No linear OOA(2765, 56, F27, 2, 64) (dual of [(56, 2), 47, 65]-NRT-code) | [i] | ||
| 14 | No linear OOA(2766, 56, F27, 2, 65) (dual of [(56, 2), 46, 66]-NRT-code) | [i] | ||
| 15 | No linear OOA(2767, 56, F27, 2, 66) (dual of [(56, 2), 45, 67]-NRT-code) | [i] | ||
| 16 | No linear OOA(2768, 56, F27, 2, 67) (dual of [(56, 2), 44, 68]-NRT-code) | [i] | ||
| 17 | No linear OOA(2769, 56, F27, 2, 68) (dual of [(56, 2), 43, 69]-NRT-code) | [i] | ||
| 18 | No linear OOA(2770, 56, F27, 2, 69) (dual of [(56, 2), 42, 70]-NRT-code) | [i] | ||
| 19 | No linear OOA(2771, 56, F27, 2, 70) (dual of [(56, 2), 41, 71]-NRT-code) | [i] | ||
| 20 | No linear OOA(2772, 56, F27, 2, 71) (dual of [(56, 2), 40, 72]-NRT-code) | [i] | ||
| 21 | No linear OOA(2773, 56, F27, 2, 72) (dual of [(56, 2), 39, 73]-NRT-code) | [i] | ||
| 22 | No linear OOA(2774, 56, F27, 2, 73) (dual of [(56, 2), 38, 74]-NRT-code) | [i] | ||
| 23 | No linear OOA(2775, 56, F27, 2, 74) (dual of [(56, 2), 37, 75]-NRT-code) | [i] | ||
| 24 | No linear OOA(2776, 56, F27, 2, 75) (dual of [(56, 2), 36, 76]-NRT-code) | [i] | ||
| 25 | No linear OOA(2777, 56, F27, 2, 76) (dual of [(56, 2), 35, 77]-NRT-code) | [i] | ||
| 26 | No linear OOA(2778, 56, F27, 2, 77) (dual of [(56, 2), 34, 78]-NRT-code) | [i] | ||
| 27 | No linear OOA(2779, 56, F27, 2, 78) (dual of [(56, 2), 33, 79]-NRT-code) | [i] | ||
| 28 | No linear OOA(2780, 56, F27, 2, 79) (dual of [(56, 2), 32, 80]-NRT-code) | [i] | ||
| 29 | No linear OOA(2781, 56, F27, 2, 80) (dual of [(56, 2), 31, 81]-NRT-code) | [i] | ||
| 30 | No linear OOA(2782, 56, F27, 2, 81) (dual of [(56, 2), 30, 82]-NRT-code) | [i] | ||
| 31 | No linear OOA(2783, 56, F27, 2, 82) (dual of [(56, 2), 29, 83]-NRT-code) | [i] | ||
| 32 | No linear OOA(2784, 56, F27, 2, 83) (dual of [(56, 2), 28, 84]-NRT-code) | [i] | ||
| 33 | No linear OOA(2785, 56, F27, 2, 84) (dual of [(56, 2), 27, 85]-NRT-code) | [i] | ||
| 34 | No linear OOA(2786, 56, F27, 2, 85) (dual of [(56, 2), 26, 86]-NRT-code) | [i] | ||
| 35 | No linear OOA(2787, 56, F27, 2, 86) (dual of [(56, 2), 25, 87]-NRT-code) | [i] | ||
| 36 | No linear OOA(2788, 56, F27, 2, 87) (dual of [(56, 2), 24, 88]-NRT-code) | [i] | ||
| 37 | No linear OOA(2789, 56, F27, 2, 88) (dual of [(56, 2), 23, 89]-NRT-code) | [i] | ||
| 38 | No linear OOA(2790, 56, F27, 2, 89) (dual of [(56, 2), 22, 90]-NRT-code) | [i] | ||
| 39 | No linear OOA(2791, 56, F27, 2, 90) (dual of [(56, 2), 21, 91]-NRT-code) | [i] | ||
| 40 | No linear OOA(2792, 56, F27, 2, 91) (dual of [(56, 2), 20, 92]-NRT-code) | [i] | ||
| 41 | No linear OOA(2793, 56, F27, 2, 92) (dual of [(56, 2), 19, 93]-NRT-code) | [i] | ||
| 42 | No linear OOA(2794, 56, F27, 2, 93) (dual of [(56, 2), 18, 94]-NRT-code) | [i] | ||
| 43 | No linear OOA(2795, 56, F27, 2, 94) (dual of [(56, 2), 17, 95]-NRT-code) | [i] | ||
| 44 | No linear OOA(2796, 56, F27, 2, 95) (dual of [(56, 2), 16, 96]-NRT-code) | [i] | ||
| 45 | No linear OOA(2797, 56, F27, 2, 96) (dual of [(56, 2), 15, 97]-NRT-code) | [i] | ||
| 46 | No linear OOA(2798, 56, F27, 2, 97) (dual of [(56, 2), 14, 98]-NRT-code) | [i] | ||
| 47 | No linear OOA(2799, 56, F27, 2, 98) (dual of [(56, 2), 13, 99]-NRT-code) | [i] | ||
| 48 | No linear OOA(27100, 56, F27, 2, 99) (dual of [(56, 2), 12, 100]-NRT-code) | [i] | ||
| 49 | No linear OOA(27101, 56, F27, 2, 100) (dual of [(56, 2), 11, 101]-NRT-code) | [i] | ||
| 50 | No linear OOA(27102, 56, F27, 2, 101) (dual of [(56, 2), 10, 102]-NRT-code) | [i] | ||
| 51 | No linear OOA(27103, 56, F27, 2, 102) (dual of [(56, 2), 9, 103]-NRT-code) | [i] | ||
| 52 | No linear OOA(27104, 56, F27, 2, 103) (dual of [(56, 2), 8, 104]-NRT-code) | [i] | ||
| 53 | No linear OOA(27105, 56, F27, 2, 104) (dual of [(56, 2), 7, 105]-NRT-code) | [i] | ||
| 54 | No linear OOA(27106, 56, F27, 2, 105) (dual of [(56, 2), 6, 106]-NRT-code) | [i] | ||
| 55 | No linear OOA(27107, 56, F27, 2, 106) (dual of [(56, 2), 5, 107]-NRT-code) | [i] | ||
| 56 | No linear OOA(27108, 56, F27, 2, 107) (dual of [(56, 2), 4, 108]-NRT-code) | [i] | ||
| 57 | No linear OOA(27109, 56, F27, 2, 108) (dual of [(56, 2), 3, 109]-NRT-code) | [i] | ||
| 58 | No linear OOA(2753, 56, F27, 2, 52) (dual of [(56, 2), 59, 53]-NRT-code) | [i] | Depth Reduction | |
| 59 | No digital (1, 53, 56)-net over F27 | [i] | Extracting Embedded Orthogonal Array | |
| 60 | No linear OA(2728, 81, F27, 27) (dual of [81, 53, 28]-code) | [i] | Dual of a Near-MDS Code Is Again a Near-MDS Code | |
| 61 | No linear OA(2754, 110, F27, 52) (dual of [110, 56, 53]-code) | [i] | Construction Y1 (Bound) | |