Information on Result #707259
Linear OA(425, 351, F4, 7) (dual of [351, 326, 8]-code), using construction XX applied to C1 = C([111,116]), C2 = C([110,115]), C3 = C1 + C2 = C([111,115]), and C∩ = C1 ∩ C2 = C([110,116]) based on
- linear OA(420, 341, F4, 6) (dual of [341, 321, 7]-code), using the BCH-code C(I) with length 341 | 45−1, defining interval I = {111,112,…,116}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(420, 341, F4, 6) (dual of [341, 321, 7]-code), using the BCH-code C(I) with length 341 | 45−1, defining interval I = {110,111,…,115}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(425, 341, F4, 7) (dual of [341, 316, 8]-code), using the BCH-code C(I) with length 341 | 45−1, defining interval I = {110,111,…,116}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(415, 341, F4, 5) (dual of [341, 326, 6]-code), using the BCH-code C(I) with length 341 | 45−1, defining interval I = {111,112,113,114,115}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code) (see above)
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(425, 351, F4, 2, 7) (dual of [(351, 2), 677, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(425, 351, F4, 3, 7) (dual of [(351, 3), 1028, 8]-NRT-code) | [i] | ||
| 3 | Digital (18, 25, 351)-net over F4 | [i] | ||
| 4 | Linear OOA(425, 175, F4, 2, 7) (dual of [(175, 2), 325, 8]-NRT-code) | [i] | OOA Folding | |