Information on Result #722272
Linear OA(16119, 286, F16, 63) (dual of [286, 167, 64]-code), using construction XX applied to C1 = C([249,51]), C2 = C([0,56]), C3 = C1 + C2 = C([0,51]), and C∩ = C1 ∩ C2 = C([249,56]) based on
- linear OA(16100, 255, F16, 58) (dual of [255, 155, 59]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−6,−5,…,51}, and designed minimum distance d ≥ |I|+1 = 59 [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(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 = {−6,−5,…,56}, and designed minimum distance d ≥ |I|+1 = 64 [i]
- linear OA(1688, 255, F16, 52) (dual of [255, 167, 53]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,51], and designed minimum distance d ≥ |I|+1 = 53 [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(164, 14, F16, 4) (dual of [14, 10, 5]-code or 14-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(16119, 143, F16, 2, 63) (dual of [(143, 2), 167, 64]-NRT-code) | [i] | OOA Folding | |