Information on Result #722106
Linear OA(16109, 284, F16, 57) (dual of [284, 175, 58]-code), using construction XX applied to C1 = C([254,50]), C2 = C([7,55]), C3 = C1 + C2 = C([7,50]), and C∩ = C1 ∩ C2 = C([254,55]) based on
- linear OA(1689, 255, F16, 52) (dual of [255, 166, 53]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,50}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(1689, 255, F16, 49) (dual of [255, 166, 50]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {7,8,…,55}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(1698, 255, F16, 57) (dual of [255, 157, 58]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,55}, and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(1680, 255, F16, 44) (dual of [255, 175, 45]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {7,8,…,50}, and designed minimum distance d ≥ |I|+1 = 45 [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(16109, 142, F16, 2, 57) (dual of [(142, 2), 175, 58]-NRT-code) | [i] | OOA Folding | |