Information on Result #714481
Linear OA(827, 70, F8, 15) (dual of [70, 43, 16]-code), using construction XX applied to C1 = C([61,11]), C2 = C([0,12]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C([61,12]) based on
- linear OA(824, 63, F8, 14) (dual of [63, 39, 15]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−2,−1,…,11}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(822, 63, F8, 13) (dual of [63, 41, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [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 = {−2,−1,…,12}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(820, 63, F8, 12) (dual of [63, 43, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(81, 5, F8, 1) (dual of [5, 4, 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, 2, F8, 0) (dual of [2, 2, 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.
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(827, 35, F8, 2, 15) (dual of [(35, 2), 43, 16]-NRT-code) | [i] | OOA Folding | |