Information on Result #714561
Linear OA(847, 84, F8, 24) (dual of [84, 37, 25]-code), using construction XX applied to C1 = C([61,18]), C2 = C([4,21]), C3 = C1 + C2 = C([4,18]), and C∩ = C1 ∩ C2 = C([61,21]) based on
- linear OA(833, 63, F8, 21) (dual of [63, 30, 22]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−2,−1,…,18}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(832, 63, F8, 18) (dual of [63, 31, 19]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {4,5,…,21}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(839, 63, F8, 24) (dual of [63, 24, 25]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {−2,−1,…,21}, and designed minimum distance d ≥ |I|+1 = 25 [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 = {4,5,…,18}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(86, 13, F8, 5) (dual of [13, 7, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 14, F8, 5) (dual of [14, 8, 6]-code), using
- extended algebraic-geometric code AGe(F,8P) [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, using
- discarding factors / shortening the dual code based on linear OA(86, 14, F8, 5) (dual of [14, 8, 6]-code), using
- linear OA(82, 8, F8, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,8)), using
- Reed–Solomon code RS(6,8) [i]
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(847, 42, F8, 2, 24) (dual of [(42, 2), 37, 25]-NRT-code) | [i] | OOA Folding | |