Information on Result #716859
Linear OA(8143, 521, F8, 54) (dual of [521, 378, 55]-code), using construction XX applied to C1 = C([509,50]), C2 = C([0,51]), C3 = C1 + C2 = C([0,50]), and C∩ = C1 ∩ C2 = C([509,51]) based on
- 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 = {−2,−1,…,50}, and designed minimum distance d ≥ |I|+1 = 54 [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(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 = {−2,−1,…,51}, and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(8133, 511, F8, 51) (dual of [511, 378, 52]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,50], and designed minimum distance d ≥ |I|+1 = 52 [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
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 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(8143, 260, F8, 2, 54) (dual of [(260, 2), 377, 55]-NRT-code) | [i] | OOA Folding | |