Information on Result #714639
Linear OA(850, 81, F8, 29) (dual of [81, 31, 30]-code), using construction XX applied to C1 = C([0,26]), C2 = C([7,28]), C3 = C1 + C2 = C([7,26]), and C∩ = C1 ∩ C2 = C([0,28]) based on
- linear OA(839, 63, F8, 27) (dual of [63, 24, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(835, 63, F8, 22) (dual of [63, 28, 23]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {7,8,…,28}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(842, 63, F8, 29) (dual of [63, 21, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(832, 63, F8, 20) (dual of [63, 31, 21]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {7,8,…,26}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(87, 14, F8, 6) (dual of [14, 7, 7]-code), using
- extended algebraic-geometric code AGe(F,7P) [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, 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 OOA(850, 40, F8, 2, 29) (dual of [(40, 2), 30, 30]-NRT-code) | [i] | OOA Folding | |