Information on Result #721774
Linear OA(1686, 280, F16, 44) (dual of [280, 194, 45]-code), using construction XX applied to C1 = C([249,34]), C2 = C([0,37]), C3 = C1 + C2 = C([0,34]), and C∩ = C1 ∩ C2 = C([249,37]) based on
- linear OA(1673, 255, F16, 41) (dual of [255, 182, 42]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−6,−5,…,34}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(1667, 255, F16, 38) (dual of [255, 188, 39]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,37], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(1679, 255, F16, 44) (dual of [255, 176, 45]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−6,−5,…,37}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(1661, 255, F16, 35) (dual of [255, 194, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(165, 17, F16, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,16)), using
- extended Reed–Solomon code RSe(12,16) [i]
- the expurgated narrow-sense BCH-code C(I) with length 17 | 162−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(162, 8, F16, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), 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(1686, 140, F16, 2, 44) (dual of [(140, 2), 194, 45]-NRT-code) | [i] | OOA Folding | |