Information on Result #675678
Linear OA(3149, 6583, F3, 27) (dual of [6583, 6434, 28]-code), using construction XX applied to Ce(27) ⊂ Ce(24) ⊂ Ce(22) based on
- linear OA(3145, 6561, F3, 28) (dual of [6561, 6416, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3129, 6561, F3, 25) (dual of [6561, 6432, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3121, 6561, F3, 23) (dual of [6561, 6440, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(31, 19, F3, 1) (dual of [19, 18, 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(3149, 3374, F3, 2, 27) (dual of [(3374, 2), 6599, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3149, 3374, F3, 3, 27) (dual of [(3374, 3), 9973, 28]-NRT-code) | [i] | ||
| 3 | Linear OOA(3149, 3374, F3, 4, 27) (dual of [(3374, 4), 13347, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(3149, 3374, F3, 5, 27) (dual of [(3374, 5), 16721, 28]-NRT-code) | [i] | ||
| 5 | Digital (122, 149, 3374)-net over F3 | [i] | ||