Information on Result #713443
Linear OA(754, 362, F7, 19) (dual of [362, 308, 20]-code), using construction XX applied to C1 = C([338,12]), C2 = C([0,14]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([338,14]) based on
- linear OA(746, 342, F7, 17) (dual of [342, 296, 18]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−4,−3,…,12}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(737, 342, F7, 15) (dual of [342, 305, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(749, 342, F7, 19) (dual of [342, 293, 20]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−4,−3,…,14}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(734, 342, F7, 13) (dual of [342, 308, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(74, 16, F7, 3) (dual of [16, 12, 4]-code or 16-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(754, 181, F7, 2, 19) (dual of [(181, 2), 308, 20]-NRT-code) | [i] | OOA Folding | |