Information on Result #716997
Linear OA(8172, 542, F8, 62) (dual of [542, 370, 63]-code), using construction XX applied to C1 = C([506,53]), C2 = C([1,56]), C3 = C1 + C2 = C([1,53]), and C∩ = C1 ∩ C2 = C([506,56]) based on
- linear OA(8157, 511, F8, 59) (dual of [511, 354, 60]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−5,−4,…,53}, and designed minimum distance d ≥ |I|+1 = 60 [i]
- linear OA(8147, 511, F8, 56) (dual of [511, 364, 57]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,56], and designed minimum distance d ≥ |I|+1 = 57 [i]
- linear OA(8163, 511, F8, 62) (dual of [511, 348, 63]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−5,−4,…,56}, and designed minimum distance d ≥ |I|+1 = 63 [i]
- linear OA(8141, 511, F8, 53) (dual of [511, 370, 54]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,53], and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(87, 23, F8, 5) (dual of [23, 16, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- 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]
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(8172, 271, F8, 2, 62) (dual of [(271, 2), 370, 63]-NRT-code) | [i] | OOA Folding | |