Information on Result #713799
Linear OA(7105, 392, F7, 34) (dual of [392, 287, 35]-code), using construction XX applied to C1 = C([334,21]), C2 = C([1,25]), C3 = C1 + C2 = C([1,21]), and C∩ = C1 ∩ C2 = C([334,25]) based on
- linear OA(776, 342, F7, 30) (dual of [342, 266, 31]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−8,−7,…,21}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(766, 342, F7, 25) (dual of [342, 276, 26]-code), using the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(788, 342, F7, 34) (dual of [342, 254, 35]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−8,−7,…,25}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(754, 342, F7, 21) (dual of [342, 288, 22]-code), using the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(713, 34, F7, 8) (dual of [34, 21, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(713, 48, F7, 8) (dual of [48, 35, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(713, 48, F7, 8) (dual of [48, 35, 9]-code), using
- linear OA(74, 16, F7, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,7)), 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(7105, 196, F7, 2, 34) (dual of [(196, 2), 287, 35]-NRT-code) | [i] | OOA Folding | |