Information on Result #722128
Linear OA(16111, 284, F16, 58) (dual of [284, 173, 59]-code), using construction XX applied to C1 = C([253,50]), C2 = C([6,55]), C3 = C1 + C2 = C([6,50]), and C∩ = C1 ∩ C2 = C([253,55]) based on
- linear OA(1691, 255, F16, 53) (dual of [255, 164, 54]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−2,−1,…,50}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(1691, 255, F16, 50) (dual of [255, 164, 51]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {6,7,…,55}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(16100, 255, F16, 58) (dual of [255, 155, 59]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−2,−1,…,55}, and designed minimum distance d ≥ |I|+1 = 59 [i]
- linear OA(1682, 255, F16, 45) (dual of [255, 173, 46]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {6,7,…,50}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(167, 16, F16, 7) (dual of [16, 9, 8]-code or 16-arc in PG(6,16)), using
- Reed–Solomon code RS(9,16) [i]
- linear OA(164, 13, F16, 4) (dual of [13, 9, 5]-code or 13-arc in PG(3,16)), using
- discarding factors / shortening the dual code based on linear OA(164, 16, F16, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)), using
- Reed–Solomon code RS(12,16) [i]
- discarding factors / shortening the dual code based on linear OA(164, 16, F16, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)), 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(16111, 142, F16, 2, 58) (dual of [(142, 2), 173, 59]-NRT-code) | [i] | OOA Folding | |