Information on Result #722317
Linear OA(16122, 283, F16, 65) (dual of [283, 161, 66]-code), using construction XX applied to C1 = C([249,54]), C2 = C([0,58]), C3 = C1 + C2 = C([0,54]), and C∩ = C1 ∩ C2 = C([249,58]) based on
- linear OA(16106, 255, F16, 61) (dual of [255, 149, 62]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−6,−5,…,54}, and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(16102, 255, F16, 59) (dual of [255, 153, 60]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,58], and designed minimum distance d ≥ |I|+1 = 60 [i]
- linear OA(16114, 255, F16, 65) (dual of [255, 141, 66]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−6,−5,…,58}, and designed minimum distance d ≥ |I|+1 = 66 [i]
- linear OA(1694, 255, F16, 55) (dual of [255, 161, 56]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,54], and designed minimum distance d ≥ |I|+1 = 56 [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(163, 11, F16, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,16) or 11-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(16122, 141, F16, 2, 65) (dual of [(141, 2), 160, 66]-NRT-code) | [i] | OOA Folding | |