Information on Result #722229
Linear OA(16114, 282, F16, 61) (dual of [282, 168, 62]-code), using construction XX applied to C1 = C([249,50]), C2 = C([0,54]), C3 = C1 + C2 = C([0,50]), and C∩ = C1 ∩ C2 = C([249,54]) based on
- linear OA(1699, 255, F16, 57) (dual of [255, 156, 58]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−6,−5,…,50}, and designed minimum distance d ≥ |I|+1 = 58 [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(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(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(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, 10, F16, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,16) or 10-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(16114, 141, F16, 2, 61) (dual of [(141, 2), 168, 62]-NRT-code) | [i] | OOA Folding | |