Information on Result #1304138
Linear OA(354, 292, F3, 14) (dual of [292, 238, 15]-code), using 32 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 12 times 0) based on linear OA(347, 253, F3, 14) (dual of [253, 206, 15]-code), using
- construction XX applied to C1 = C([109,121]), C2 = C([111,122]), C3 = C1 + C2 = C([111,121]), and C∩ = C1 ∩ C2 = C([109,122]) [i] based on
- linear OA(341, 242, F3, 13) (dual of [242, 201, 14]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {109,110,…,121}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(341, 242, F3, 12) (dual of [242, 201, 13]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {111,112,…,122}, and designed minimum distance d ≥ |I|+1 = 13 [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 = {109,110,…,122}, and designed minimum distance d ≥ |I|+1 = 15 [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 = {111,112,…,121}, and designed minimum distance d ≥ |I|+1 = 12 [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(354, 292, F3, 2, 14) (dual of [(292, 2), 530, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(354, 292, F3, 3, 14) (dual of [(292, 3), 822, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(354, 292, F3, 4, 14) (dual of [(292, 4), 1114, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(354, 292, F3, 5, 14) (dual of [(292, 5), 1406, 15]-NRT-code) | [i] | ||
| 5 | Digital (40, 54, 292)-net over F3 | [i] | ||