Information on Result #715180
Linear OA(844, 521, F8, 16) (dual of [521, 477, 17]-code), using construction XX applied to C1 = C([509,12]), C2 = C([0,13]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([509,13]) based on
- linear OA(840, 511, F8, 15) (dual of [511, 471, 16]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−2,−1,…,12}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(837, 511, F8, 14) (dual of [511, 474, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(843, 511, F8, 16) (dual of [511, 468, 17]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−2,−1,…,13}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(834, 511, F8, 13) (dual of [511, 477, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [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(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(844, 505, F8, 2, 16) (dual of [(505, 2), 966, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(844, 505, F8, 3, 16) (dual of [(505, 3), 1471, 17]-NRT-code) | [i] | ||
| 3 | Digital (28, 44, 505)-net over F8 | [i] | ||
| 4 | Linear OOA(844, 260, F8, 2, 16) (dual of [(260, 2), 476, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(844, 173, F8, 3, 16) (dual of [(173, 3), 475, 17]-NRT-code) | [i] | ||