Information on Result #717462
Linear OA(8106, 832, F8, 31) (dual of [832, 726, 32]-code), using construction XX applied to C1 = C([817,27]), C2 = C([0,28]), C3 = C1 + C2 = C([0,27]), and C∩ = C1 ∩ C2 = C([817,28]) based on
- linear OA(8101, 819, F8, 30) (dual of [819, 718, 31]-code), using the BCH-code C(I) with length 819 | 84−1, defining interval I = {−2,−1,…,27}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(897, 819, F8, 29) (dual of [819, 722, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 819 | 84−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(8105, 819, F8, 31) (dual of [819, 714, 32]-code), using the BCH-code C(I) with length 819 | 84−1, defining interval I = {−2,−1,…,28}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(893, 819, F8, 28) (dual of [819, 726, 29]-code), using the expurgated narrow-sense BCH-code C(I) with length 819 | 84−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(81, 9, F8, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- linear OA(80, 4, F8, 0) (dual of [4, 4, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(8106, 416, F8, 2, 31) (dual of [(416, 2), 726, 32]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8106, 277, F8, 3, 31) (dual of [(277, 3), 725, 32]-NRT-code) | [i] | ||