Information on Result #722037
Linear OA(16111, 288, F16, 57) (dual of [288, 177, 58]-code), using construction XX applied to C1 = C([253,50]), C2 = C([8,54]), C3 = C1 + C2 = C([8,50]), and C∩ = C1 ∩ C2 = C([253,54]) 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(1685, 255, F16, 47) (dual of [255, 170, 48]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {8,9,…,54}, and designed minimum distance d ≥ |I|+1 = 48 [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 = {−2,−1,…,54}, and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(1678, 255, F16, 43) (dual of [255, 177, 44]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {8,9,…,50}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(1610, 23, F16, 9) (dual of [23, 13, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(1610, 24, F16, 9) (dual of [24, 14, 10]-code), using
- extended algebraic-geometric code AGe(F,14P) [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- discarding factors / shortening the dual code based on linear OA(1610, 24, F16, 9) (dual of [24, 14, 10]-code), using
- linear OA(163, 10, F16, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,16) or 10-cap in PG(2,16)), using
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- Reed–Solomon code RS(13,16) [i]
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), 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, 144, F16, 2, 57) (dual of [(144, 2), 177, 58]-NRT-code) | [i] | OOA Folding | |