Information on Result #703100
Linear OA(327, 253, F3, 8) (dual of [253, 226, 9]-code), using construction XX applied to C1 = C([115,121]), C2 = C([117,122]), C3 = C1 + C2 = C([117,121]), and C∩ = C1 ∩ C2 = C([115,122]) based on
- linear OA(321, 242, F3, 7) (dual of [242, 221, 8]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {115,116,…,121}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(321, 242, F3, 6) (dual of [242, 221, 7]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {117,118,…,122}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(326, 242, F3, 8) (dual of [242, 216, 9]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {115,116,…,122}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(316, 242, F3, 5) (dual of [242, 226, 6]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {117,118,119,120,121}, and designed minimum distance d ≥ |I|+1 = 6 [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(327, 170, F3, 2, 8) (dual of [(170, 2), 313, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(327, 170, F3, 3, 8) (dual of [(170, 3), 483, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(327, 170, F3, 4, 8) (dual of [(170, 4), 653, 9]-NRT-code) | [i] | ||
| 4 | Linear OOA(327, 170, F3, 5, 8) (dual of [(170, 5), 823, 9]-NRT-code) | [i] | ||
| 5 | Digital (19, 27, 170)-net over F3 | [i] | ||
| 6 | Linear OOA(327, 126, F3, 2, 8) (dual of [(126, 2), 225, 9]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(327, 84, F3, 3, 8) (dual of [(84, 3), 225, 9]-NRT-code) | [i] | ||
| 8 | Linear OOA(327, 63, F3, 4, 8) (dual of [(63, 4), 225, 9]-NRT-code) | [i] | ||