Information on Result #722045
Linear OA(16113, 294, F16, 57) (dual of [294, 181, 58]-code), using construction XX applied to C1 = C([0,50]), C2 = C([10,56]), C3 = C1 + C2 = C([10,50]), and C∩ = C1 ∩ C2 = C([0,56]) based on
- linear OA(1687, 255, F16, 51) (dual of [255, 168, 52]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,50], and designed minimum distance d ≥ |I|+1 = 52 [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 = {10,11,…,56}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(1698, 255, F16, 57) (dual of [255, 157, 58]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,56], and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(1674, 255, F16, 41) (dual of [255, 181, 42]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {10,11,…,50}, and designed minimum distance d ≥ |I|+1 = 42 [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(165, 16, F16, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,16)), using
- Reed–Solomon code RS(11,16) [i]
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(16113, 147, F16, 2, 57) (dual of [(147, 2), 181, 58]-NRT-code) | [i] | OOA Folding | |