Information on Result #716579
Linear OA(8129, 525, F8, 48) (dual of [525, 396, 49]-code), using construction XX applied to C1 = C([509,43]), C2 = C([0,45]), C3 = C1 + C2 = C([0,43]), and C∩ = C1 ∩ C2 = C([509,45]) based on
- linear OA(8121, 511, F8, 46) (dual of [511, 390, 47]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−2,−1,…,43}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(8121, 511, F8, 46) (dual of [511, 390, 47]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,45], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(8127, 511, F8, 48) (dual of [511, 384, 49]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−2,−1,…,45}, and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(8115, 511, F8, 44) (dual of [511, 396, 45]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,43], and designed minimum distance d ≥ |I|+1 = 45 [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(8129, 262, F8, 2, 48) (dual of [(262, 2), 395, 49]-NRT-code) | [i] | OOA Folding | |