Information on Result #722064
Linear OA(16104, 276, F16, 56) (dual of [276, 172, 57]-code), using construction XX applied to C1 = C([253,51]), C2 = C([6,53]), C3 = C1 + C2 = C([6,51]), and C∩ = C1 ∩ C2 = C([253,53]) 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(1687, 255, F16, 48) (dual of [255, 168, 49]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {6,7,…,53}, and designed minimum distance d ≥ |I|+1 = 49 [i]
- linear OA(1696, 255, F16, 56) (dual of [255, 159, 57]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−2,−1,…,53}, and designed minimum distance d ≥ |I|+1 = 57 [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(161, 5, F16, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, 16, F16, 1) (dual of [16, 15, 2]-code), using
- Reed–Solomon code RS(15,16) [i]
- discarding factors / shortening the dual code based on linear OA(161, 16, F16, 1) (dual of [16, 15, 2]-code), 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(16104, 138, F16, 2, 56) (dual of [(138, 2), 172, 57]-NRT-code) | [i] | OOA Folding | |