Information on Result #715667
Linear OA(875, 523, F8, 28) (dual of [523, 448, 29]-code), using construction XX applied to C1 = C([509,24]), C2 = C([1,25]), C3 = C1 + C2 = C([1,24]), and C∩ = C1 ∩ C2 = C([509,25]) based on
- linear OA(870, 511, F8, 27) (dual of [511, 441, 28]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−2,−1,…,24}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(866, 511, F8, 25) (dual of [511, 445, 26]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(873, 511, F8, 28) (dual of [511, 438, 29]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−2,−1,…,25}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(863, 511, F8, 24) (dual of [511, 448, 25]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(82, 9, F8, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,8)), using
- extended Reed–Solomon code RSe(7,8) [i]
- Hamming code H(2,8) [i]
- 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(875, 261, F8, 2, 28) (dual of [(261, 2), 447, 29]-NRT-code) | [i] | OOA Folding | |