Information on Result #717440
Linear OA(8104, 836, F8, 30) (dual of [836, 732, 31]-code), using construction XX applied to C1 = C([816,25]), C2 = C([0,26]), C3 = C1 + C2 = C([0,25]), and C∩ = C1 ∩ C2 = C([816,26]) based on
- linear OA(899, 819, F8, 29) (dual of [819, 720, 30]-code), using the BCH-code C(I) with length 819 | 84−1, defining interval I = {−3,−2,…,25}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(889, 819, F8, 27) (dual of [819, 730, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 819 | 84−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 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 = {−3,−2,…,26}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(887, 819, F8, 26) (dual of [819, 732, 27]-code), using the expurgated narrow-sense BCH-code C(I) with length 819 | 84−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(83, 15, F8, 2) (dual of [15, 12, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(8104, 418, F8, 2, 30) (dual of [(418, 2), 732, 31]-NRT-code) | [i] | OOA Folding | |