Information on Result #721720
Linear OA(1675, 272, F16, 39) (dual of [272, 197, 40]-code), using construction XX applied to C1 = C([252,34]), C2 = C([4,35]), C3 = C1 + C2 = C([4,34]), and C∩ = C1 ∩ C2 = C([252,35]) based on
- linear OA(1667, 255, F16, 38) (dual of [255, 188, 39]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−3,−2,…,34}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(1660, 255, F16, 32) (dual of [255, 195, 33]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {4,5,…,35}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(1669, 255, F16, 39) (dual of [255, 186, 40]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−3,−2,…,35}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(1658, 255, F16, 31) (dual of [255, 197, 32]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {4,5,…,34}, and designed minimum distance d ≥ |I|+1 = 32 [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(1675, 136, F16, 2, 39) (dual of [(136, 2), 197, 40]-NRT-code) | [i] | OOA Folding | |