Information on Result #721570
Linear OA(1641, 262, F16, 22) (dual of [262, 221, 23]-code), using construction XX applied to C1 = C([253,18]), C2 = C([0,19]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([253,19]) based on
- linear OA(1638, 255, F16, 21) (dual of [255, 217, 22]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−2,−1,…,18}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(1636, 255, F16, 20) (dual of [255, 219, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(1640, 255, F16, 22) (dual of [255, 215, 23]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−2,−1,…,19}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(1634, 255, F16, 19) (dual of [255, 221, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(161, 5, F16, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, 16, F16, 1) (dual of [16, 15, 2]-code), using
- Reed–Solomon code RS(15,16) [i]
- discarding factors / shortening the dual code based on linear OA(161, 16, F16, 1) (dual of [16, 15, 2]-code), using
- linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 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 | OA(855, 262, S8, 22) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(1641, 131, F16, 2, 22) (dual of [(131, 2), 221, 23]-NRT-code) | [i] | OOA Folding | |