Information on Result #677022
Linear OA(3113, 747, F3, 27) (dual of [747, 634, 28]-code), using construction XX applied to Ce(27) ⊂ Ce(24) ⊂ Ce(22) based on
- linear OA(3109, 729, F3, 28) (dual of [729, 620, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(397, 729, F3, 25) (dual of [729, 632, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(391, 729, F3, 23) (dual of [729, 638, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(31, 3, F3, 1) (dual of [3, 2, 2]-code), using
- Reed–Solomon code RS(2,3) [i]
Mode: Constructive and 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 | Linear OOA(3113, 676, F3, 2, 27) (dual of [(676, 2), 1239, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3113, 676, F3, 3, 27) (dual of [(676, 3), 1915, 28]-NRT-code) | [i] | ||
| 3 | Linear OOA(3113, 676, F3, 4, 27) (dual of [(676, 4), 2591, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(3113, 676, F3, 5, 27) (dual of [(676, 5), 3267, 28]-NRT-code) | [i] | ||
| 5 | Digital (86, 113, 676)-net over F3 | [i] | ||