Information on Result #714145
Linear OA(7104, 352, F7, 40) (dual of [352, 248, 41]-code), using construction XX applied to C1 = C([340,36]), C2 = C([0,37]), C3 = C1 + C2 = C([0,36]), and C∩ = C1 ∩ C2 = C([340,37]) based on
- linear OA(7100, 342, F7, 39) (dual of [342, 242, 40]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−2,−1,…,36}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(797, 342, F7, 38) (dual of [342, 245, 39]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,37], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(7103, 342, F7, 40) (dual of [342, 239, 41]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−2,−1,…,37}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(794, 342, F7, 37) (dual of [342, 248, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [i]
- 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(7104, 176, F7, 2, 40) (dual of [(176, 2), 248, 41]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(7104, 117, F7, 3, 40) (dual of [(117, 3), 247, 41]-NRT-code) | [i] | ||