Information on Result #722156
Linear OA(16114, 288, F16, 59) (dual of [288, 174, 60]-code), using construction XX applied to C1 = C([254,51]), C2 = C([7,57]), C3 = C1 + C2 = C([7,51]), and C∩ = C1 ∩ C2 = C([254,57]) based on
- linear OA(1690, 255, F16, 53) (dual of [255, 165, 54]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,51}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(1693, 255, F16, 51) (dual of [255, 162, 52]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {7,8,…,57}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(16102, 255, F16, 59) (dual of [255, 153, 60]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−1,0,…,57}, and designed minimum distance d ≥ |I|+1 = 60 [i]
- linear OA(1681, 255, F16, 45) (dual of [255, 174, 46]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {7,8,…,51}, and designed minimum distance d ≥ |I|+1 = 46 [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(16114, 144, F16, 2, 59) (dual of [(144, 2), 174, 60]-NRT-code) | [i] | OOA Folding | |