Information on Result #714446
Linear OA(815, 67, F8, 8) (dual of [67, 52, 9]-code), using construction XX applied to C1 = C([62,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([62,6]) based on
- 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 = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(813, 63, F8, 7) (dual of [63, 50, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [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 = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- 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
- linear OA(80, 2, F8, 0) (dual of [2, 2, 1]-code) (see above)
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(8170, 2097219, F8, 26) (dual of [2097219, 2097049, 27]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 2 | Linear OA(8163, 2097219, F8, 24) (dual of [2097219, 2097056, 25]-code) | [i] | ||
| 3 | Linear OA(8156, 2097219, F8, 23) (dual of [2097219, 2097063, 24]-code) | [i] | ||
| 4 | Linear OA(8149, 2097219, F8, 22) (dual of [2097219, 2097070, 23]-code) | [i] | ||
| 5 | Linear OA(8142, 2097219, F8, 21) (dual of [2097219, 2097077, 22]-code) | [i] | ||
| 6 | Linear OA(8135, 2097219, F8, 20) (dual of [2097219, 2097084, 21]-code) | [i] | ||
| 7 | Linear OOA(815, 33, F8, 2, 8) (dual of [(33, 2), 51, 9]-NRT-code) | [i] | OOA Folding | |