Information on Result #716817
Linear OA(8141, 525, F8, 53) (dual of [525, 384, 54]-code), using construction XX applied to C1 = C([509,48]), C2 = C([0,50]), C3 = C1 + C2 = C([0,48]), and C∩ = C1 ∩ C2 = C([509,50]) based on
- linear OA(8133, 511, F8, 51) (dual of [511, 378, 52]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−2,−1,…,48}, and designed minimum distance d ≥ |I|+1 = 52 [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(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(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(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(81, 7, F8, 1) (dual of [7, 6, 2]-code) (see above)
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(8141, 262, F8, 2, 53) (dual of [(262, 2), 383, 54]-NRT-code) | [i] | OOA Folding | |