Information on Result #716748
Linear OA(8144, 531, F8, 53) (dual of [531, 387, 54]-code), using construction XX applied to C1 = C([507,46]), C2 = C([0,48]), C3 = C1 + C2 = C([0,46]), and C∩ = C1 ∩ C2 = C([507,48]) based on
- linear OA(8136, 511, F8, 51) (dual of [511, 375, 52]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−4,−3,…,46}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(8127, 511, F8, 49) (dual of [511, 384, 50]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,48], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(8139, 511, F8, 53) (dual of [511, 372, 54]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−4,−3,…,48}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(8124, 511, F8, 47) (dual of [511, 387, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,46], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(84, 16, F8, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,8)), using
- linear OA(81, 4, F8, 1) (dual of [4, 3, 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(8144, 265, F8, 2, 53) (dual of [(265, 2), 386, 54]-NRT-code) | [i] | OOA Folding | |