Information on Result #703222
Linear OA(357, 253, F3, 17) (dual of [253, 196, 18]-code), using construction XX applied to C1 = C([106,121]), C2 = C([108,122]), C3 = C1 + C2 = C([108,121]), and C∩ = C1 ∩ C2 = C([106,122]) based on
- linear OA(351, 242, F3, 16) (dual of [242, 191, 17]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {106,107,…,121}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(351, 242, F3, 15) (dual of [242, 191, 16]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {108,109,…,122}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(356, 242, F3, 17) (dual of [242, 186, 18]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {106,107,…,122}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(346, 242, F3, 14) (dual of [242, 196, 15]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {108,109,…,121}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(31, 6, F3, 1) (dual of [6, 5, 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(30, 5, F3, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
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(357, 182, F3, 2, 17) (dual of [(182, 2), 307, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(357, 182, F3, 3, 17) (dual of [(182, 3), 489, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(357, 182, F3, 4, 17) (dual of [(182, 4), 671, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(357, 182, F3, 5, 17) (dual of [(182, 5), 853, 18]-NRT-code) | [i] | ||
| 5 | Digital (40, 57, 182)-net over F3 | [i] | ||
| 6 | Linear OA(362, 269, F3, 17) (dual of [269, 207, 18]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(363, 278, F3, 17) (dual of [278, 215, 18]-code) | [i] | ||
| 8 | Linear OOA(357, 126, F3, 2, 17) (dual of [(126, 2), 195, 18]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(357, 84, F3, 3, 17) (dual of [(84, 3), 195, 18]-NRT-code) | [i] | ||