Information on Result #714505
Linear OA(836, 76, F8, 20) (dual of [76, 40, 21]-code), using construction XX applied to C1 = C([0,17]), C2 = C([5,19]), C3 = C1 + C2 = C([5,17]), and C∩ = C1 ∩ C2 = C([0,19]) based on
- linear OA(828, 63, F8, 18) (dual of [63, 35, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(826, 63, F8, 15) (dual of [63, 37, 16]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {5,6,…,19}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(831, 63, F8, 20) (dual of [63, 32, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(823, 63, F8, 13) (dual of [63, 40, 14]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {5,6,…,17}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(84, 9, F8, 4) (dual of [9, 5, 5]-code or 9-arc in PG(3,8)), using
- extended Reed–Solomon code RSe(5,8) [i]
- linear OA(81, 4, F8, 1) (dual of [4, 3, 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(836, 38, F8, 2, 20) (dual of [(38, 2), 40, 21]-NRT-code) | [i] | OOA Folding | |