Information on Result #713237
Linear OA(733, 360, F7, 11) (dual of [360, 327, 12]-code), using construction XX applied to C1 = C([339,5]), C2 = C([1,7]), C3 = C1 + C2 = C([1,5]), and C∩ = C1 ∩ C2 = C([339,7]) based on
- linear OA(725, 342, F7, 9) (dual of [342, 317, 10]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−3,−2,…,5}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(718, 342, F7, 7) (dual of [342, 324, 8]-code), using the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(728, 342, F7, 11) (dual of [342, 314, 12]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−3,−2,…,7}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(715, 342, F7, 5) (dual of [342, 327, 6]-code), using the primitive narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(74, 14, F7, 3) (dual of [14, 10, 4]-code or 14-cap in PG(3,7)), using
- linear OA(71, 4, F7, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [i]
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), 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(733, 120, F7, 3, 11) (dual of [(120, 3), 327, 12]-NRT-code) | [i] | OOA Folding | |