Information on Result #714940
Linear OA(822, 527, F8, 7) (dual of [527, 505, 8]-code), using construction XX applied to C1 = C([508,1]), C2 = C([0,3]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([508,3]) based on
- linear OA(813, 511, F8, 5) (dual of [511, 498, 6]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−3,−2,−1,0,1}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(810, 511, F8, 4) (dual of [511, 501, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(819, 511, F8, 7) (dual of [511, 492, 8]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−3,−2,…,3}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(84, 511, F8, 2) (dual of [511, 507, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(82, 9, F8, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,8)), using
- extended Reed–Solomon code RSe(7,8) [i]
- Hamming code H(2,8) [i]
- linear OA(81, 7, F8, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- Reed–Solomon code RS(7,8) [i]
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 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(822, 263, F8, 2, 7) (dual of [(263, 2), 504, 8]-NRT-code) | [i] | OOA Folding | |