Information on Result #716860
Linear OA(8153, 534, F8, 56) (dual of [534, 381, 57]-code), using construction XX applied to C1 = C([507,49]), C2 = C([0,51]), C3 = C1 + C2 = C([0,49]), and C∩ = C1 ∩ C2 = C([507,51]) based on
- linear OA(8142, 511, F8, 54) (dual of [511, 369, 55]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−4,−3,…,49}, and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(8136, 511, F8, 52) (dual of [511, 375, 53]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,51], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(8148, 511, F8, 56) (dual of [511, 363, 57]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−4,−3,…,51}, and designed minimum distance d ≥ |I|+1 = 57 [i]
- linear OA(8130, 511, F8, 50) (dual of [511, 381, 51]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,49], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(84, 16, F8, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,8)), using
- 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(8153, 267, F8, 2, 56) (dual of [(267, 2), 381, 57]-NRT-code) | [i] | OOA Folding | |