Information on Result #713230
Linear OA(729, 358, F7, 10) (dual of [358, 329, 11]-code), using construction XX applied to C1 = C([49,57]), C2 = C([53,58]), C3 = C1 + C2 = C([53,57]), and C∩ = C1 ∩ C2 = C([49,58]) based on
- linear OA(722, 342, F7, 9) (dual of [342, 320, 10]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {49,50,…,57}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(716, 342, F7, 6) (dual of [342, 326, 7]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {53,54,…,58}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(725, 342, F7, 10) (dual of [342, 317, 11]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {49,50,…,58}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(713, 342, F7, 5) (dual of [342, 329, 6]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {53,54,55,56,57}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(74, 13, F7, 3) (dual of [13, 9, 4]-code or 13-cap in PG(3,7)), using
- linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 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(729, 179, F7, 2, 10) (dual of [(179, 2), 329, 11]-NRT-code) | [i] | OOA Folding | |