Information on Result #715336
Linear OA(854, 523, F8, 20) (dual of [523, 469, 21]-code), using construction XX applied to C1 = C([509,16]), C2 = C([1,17]), C3 = C1 + C2 = C([1,16]), and C∩ = C1 ∩ C2 = C([509,17]) based on
- linear OA(849, 511, F8, 19) (dual of [511, 462, 20]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−2,−1,…,16}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(845, 511, F8, 17) (dual of [511, 466, 18]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(852, 511, F8, 20) (dual of [511, 459, 21]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−2,−1,…,17}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(842, 511, F8, 16) (dual of [511, 469, 17]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(854, 261, F8, 2, 20) (dual of [(261, 2), 468, 21]-NRT-code) | [i] | OOA Folding | |