Information on Result #721687
Linear OA(1671, 272, F16, 37) (dual of [272, 201, 38]-code), using construction XX applied to C1 = C([254,34]), C2 = C([6,35]), C3 = C1 + C2 = C([6,34]), and C∩ = C1 ∩ C2 = C([254,35]) based on
- linear OA(1663, 255, F16, 36) (dual of [255, 192, 37]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,34}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(1656, 255, F16, 30) (dual of [255, 199, 31]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {6,7,…,35}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(1665, 255, F16, 37) (dual of [255, 190, 38]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,35}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(1654, 255, F16, 29) (dual of [255, 201, 30]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {6,7,…,34}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(166, 15, F16, 6) (dual of [15, 9, 7]-code or 15-arc in PG(5,16)), using
- discarding factors / shortening the dual code based on linear OA(166, 16, F16, 6) (dual of [16, 10, 7]-code or 16-arc in PG(5,16)), using
- Reed–Solomon code RS(10,16) [i]
- discarding factors / shortening the dual code based on linear OA(166, 16, F16, 6) (dual of [16, 10, 7]-code or 16-arc in PG(5,16)), 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 | Linear OOA(1671, 136, F16, 2, 37) (dual of [(136, 2), 201, 38]-NRT-code) | [i] | OOA Folding | |