Information on Result #716742
Linear OA(8168, 567, F8, 57) (dual of [567, 399, 58]-code), using construction XX applied to C1 = C([503,42]), C2 = C([0,48]), C3 = C1 + C2 = C([0,42]), and C∩ = C1 ∩ C2 = C([503,48]) based on
- linear OA(8133, 511, F8, 51) (dual of [511, 378, 52]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−8,−7,…,42}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(8127, 511, F8, 49) (dual of [511, 384, 50]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,48], and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(8148, 511, F8, 57) (dual of [511, 363, 58]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−8,−7,…,48}, and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(8112, 511, F8, 43) (dual of [511, 399, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(813, 34, F8, 7) (dual of [34, 21, 8]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(813, 63, F8, 7) (dual of [63, 50, 8]-code), using
- linear OA(87, 22, F8, 5) (dual of [22, 15, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), 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(8168, 283, F8, 2, 57) (dual of [(283, 2), 398, 58]-NRT-code) | [i] | OOA Folding | |