Information on Result #722245
Linear OA(16122, 291, F16, 63) (dual of [291, 169, 64]-code), using construction XX applied to C1 = C([248,50]), C2 = C([1,55]), C3 = C1 + C2 = C([1,50]), and C∩ = C1 ∩ C2 = C([248,55]) based on
- linear OA(16101, 255, F16, 58) (dual of [255, 154, 59]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−7,−6,…,50}, and designed minimum distance d ≥ |I|+1 = 59 [i]
- linear OA(1695, 255, F16, 55) (dual of [255, 160, 56]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,55], and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(16110, 255, F16, 63) (dual of [255, 145, 64]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−7,−6,…,55}, and designed minimum distance d ≥ |I|+1 = 64 [i]
- linear OA(1686, 255, F16, 50) (dual of [255, 169, 51]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(168, 23, F16, 7) (dual of [23, 15, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(168, 24, F16, 7) (dual of [24, 16, 8]-code), using
- extended algebraic-geometric code AGe(F,16P) [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(168, 24, F16, 7) (dual of [24, 16, 8]-code), using
- 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 OA(16121, 290, F16, 62) (dual of [290, 169, 63]-code) | [i] | Truncation | |