Information on Result #717085
Linear OA(8167, 521, F8, 63) (dual of [521, 354, 64]-code), using construction XX applied to C1 = C([509,59]), C2 = C([0,60]), C3 = C1 + C2 = C([0,59]), and C∩ = C1 ∩ C2 = C([509,60]) based on
- 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 = {−2,−1,…,59}, and designed minimum distance d ≥ |I|+1 = 63 [i]
- linear OA(8160, 511, F8, 61) (dual of [511, 351, 62]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,60], and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(8166, 511, F8, 63) (dual of [511, 345, 64]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−2,−1,…,60}, and designed minimum distance d ≥ |I|+1 = 64 [i]
- linear OA(8157, 511, F8, 60) (dual of [511, 354, 61]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,59], and designed minimum distance d ≥ |I|+1 = 61 [i]
- linear OA(81, 7, F8, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- Reed–Solomon code RS(7,8) [i]
- discarding factors / shortening the dual code based on linear OA(81, 8, F8, 1) (dual of [8, 7, 2]-code), using
- linear OA(80, 3, F8, 0) (dual of [3, 3, 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(8167, 260, F8, 2, 63) (dual of [(260, 2), 353, 64]-NRT-code) | [i] | OOA Folding | |