Information on Result #703127
Linear OA(340, 262, F3, 11) (dual of [262, 222, 12]-code), using construction XX applied to C1 = C([112,120]), C2 = C([115,122]), C3 = C1 + C2 = C([115,120]), and C∩ = C1 ∩ C2 = C([112,122]) based on
- linear OA(330, 242, F3, 9) (dual of [242, 212, 10]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {112,113,…,120}, and designed minimum distance d ≥ |I|+1 = 10 [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(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(320, 242, F3, 6) (dual of [242, 222, 7]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {115,116,…,120}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- linear OA(31, 7, F3, 1) (dual of [7, 6, 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
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(340, 235, F3, 2, 11) (dual of [(235, 2), 430, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(340, 235, F3, 3, 11) (dual of [(235, 3), 665, 12]-NRT-code) | [i] | ||
| 3 | Linear OOA(340, 235, F3, 4, 11) (dual of [(235, 4), 900, 12]-NRT-code) | [i] | ||
| 4 | Linear OOA(340, 235, F3, 5, 11) (dual of [(235, 5), 1135, 12]-NRT-code) | [i] | ||
| 5 | Digital (29, 40, 235)-net over F3 | [i] | ||
| 6 | Linear OA(341, 264, F3, 11) (dual of [264, 223, 12]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(340, 131, F3, 2, 11) (dual of [(131, 2), 222, 12]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(340, 87, F3, 3, 11) (dual of [(87, 3), 221, 12]-NRT-code) | [i] | ||