Information on Result #714841
Linear OA(869, 84, F8, 47) (dual of [84, 15, 48]-code), using construction XX applied to C1 = C([54,35]), C2 = C([0,37]), C3 = C1 + C2 = C([0,35]), and C∩ = C1 ∩ C2 = C([54,37]) based on
- linear OA(855, 63, F8, 45) (dual of [63, 8, 46]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−9,−8,…,35}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(851, 63, F8, 38) (dual of [63, 12, 39]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,37], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(858, 63, F8, 47) (dual of [63, 5, 48]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−9,−8,…,37}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(848, 63, F8, 36) (dual of [63, 15, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(810, 17, F8, 8) (dual of [17, 7, 9]-code), using
- extended algebraic-geometric code AGe(F,8P) [i] based on function field F/F8 with g(F) = 2 and N(F) ≥ 17, using
- 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 OA(870, 86, F8, 47) (dual of [86, 16, 48]-code) | [i] | Construction X with Varšamov Bound | |
| 2 | Linear OOA(869, 42, F8, 2, 47) (dual of [(42, 2), 15, 48]-NRT-code) | [i] | OOA Folding | |