Information on Result #703142
Linear OA(337, 253, F3, 11) (dual of [253, 216, 12]-code), using construction XX applied to C1 = C([112,121]), C2 = C([114,122]), C3 = C1 + C2 = C([114,121]), and C∩ = C1 ∩ C2 = C([112,122]) based on
- linear OA(331, 242, F3, 10) (dual of [242, 211, 11]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {112,113,…,121}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(331, 242, F3, 9) (dual of [242, 211, 10]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {114,115,…,122}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(336, 242, F3, 11) (dual of [242, 206, 12]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {112,113,…,122}, and designed minimum distance d ≥ |I|+1 = 12 [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 = {114,115,…,121}, and designed minimum distance d ≥ |I|+1 = 9 [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(337, 161, F3, 2, 11) (dual of [(161, 2), 285, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(337, 161, F3, 3, 11) (dual of [(161, 3), 446, 12]-NRT-code) | [i] | ||
| 3 | Linear OOA(337, 161, F3, 4, 11) (dual of [(161, 4), 607, 12]-NRT-code) | [i] | ||
| 4 | Linear OOA(337, 161, F3, 5, 11) (dual of [(161, 5), 768, 12]-NRT-code) | [i] | ||
| 5 | Digital (26, 37, 161)-net over F3 | [i] | ||
| 6 | Linear OA(341, 265, F3, 11) (dual of [265, 224, 12]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(342, 274, F3, 11) (dual of [274, 232, 12]-code) | [i] | ||
| 8 | Linear OOA(337, 126, F3, 2, 11) (dual of [(126, 2), 215, 12]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(337, 84, F3, 3, 11) (dual of [(84, 3), 215, 12]-NRT-code) | [i] | ||
| 10 | Linear OOA(337, 63, F3, 4, 11) (dual of [(63, 4), 215, 12]-NRT-code) | [i] | ||