Information on Result #1304106
Linear OA(341, 265, F3, 11) (dual of [265, 224, 12]-code), using 8 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 0, 0, 0) based on 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]) [i] 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: 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(341, 265, F3, 2, 11) (dual of [(265, 2), 489, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(341, 265, F3, 3, 11) (dual of [(265, 3), 754, 12]-NRT-code) | [i] | ||
| 3 | Linear OOA(341, 265, F3, 4, 11) (dual of [(265, 4), 1019, 12]-NRT-code) | [i] | ||
| 4 | Linear OOA(341, 265, F3, 5, 11) (dual of [(265, 5), 1284, 12]-NRT-code) | [i] | ||
| 5 | Digital (30, 41, 265)-net over F3 | [i] | ||