Information on Result #714454
Linear OA(820, 70, F8, 11) (dual of [70, 50, 12]-code), using construction XX applied to C1 = C([0,9]), C2 = C([3,10]), C3 = C1 + C2 = C([3,9]), and C∩ = C1 ∩ C2 = C([0,10]) based on
- linear OA(816, 63, F8, 10) (dual of [63, 47, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(815, 63, F8, 8) (dual of [63, 48, 9]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {3,4,…,10}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(818, 63, F8, 11) (dual of [63, 45, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(813, 63, F8, 7) (dual of [63, 50, 8]-code), using the primitive BCH-code C(I) with length 63 = 82−1, defining interval I = {3,4,…,9}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(82, 5, F8, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,8)), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(82, 8, F8, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,8)), 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 OA(8171, 32839, F8, 35) (dual of [32839, 32668, 36]-code) | [i] | Construction X with Cyclic Codes | |
| 2 | Linear OA(8161, 32839, F8, 33) (dual of [32839, 32678, 34]-code) | [i] | ||
| 3 | Linear OA(8166, 32838, F8, 34) (dual of [32838, 32672, 35]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 4 | Linear OA(8136, 32838, F8, 27) (dual of [32838, 32702, 28]-code) | [i] | ||
| 5 | Linear OA(8131, 32838, F8, 26) (dual of [32838, 32707, 27]-code) | [i] | ||
| 6 | Linear OA(8126, 32838, F8, 25) (dual of [32838, 32712, 26]-code) | [i] | ||
| 7 | Linear OOA(820, 35, F8, 2, 11) (dual of [(35, 2), 50, 12]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(820, 23, F8, 3, 11) (dual of [(23, 3), 49, 12]-NRT-code) | [i] | ||