Information on Result #722170
Linear OA(16116, 288, F16, 60) (dual of [288, 172, 61]-code), using construction XX applied to C1 = C([253,51]), C2 = C([6,57]), C3 = C1 + C2 = C([6,51]), and C∩ = C1 ∩ C2 = C([253,57]) based on
- linear OA(1692, 255, F16, 54) (dual of [255, 163, 55]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−2,−1,…,51}, and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(1695, 255, F16, 52) (dual of [255, 160, 53]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {6,7,…,57}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(16104, 255, F16, 60) (dual of [255, 151, 61]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−2,−1,…,57}, and designed minimum distance d ≥ |I|+1 = 61 [i]
- linear OA(1683, 255, F16, 46) (dual of [255, 172, 47]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {6,7,…,51}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(167, 16, F16, 7) (dual of [16, 9, 8]-code or 16-arc in PG(6,16)), using
- Reed–Solomon code RS(9,16) [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]
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(16116, 144, F16, 2, 60) (dual of [(144, 2), 172, 61]-NRT-code) | [i] | OOA Folding | |