Information on Result #722175
Linear OA(1695, 262, F16, 55) (dual of [262, 167, 56]-code), using construction XX applied to C1 = C([253,51]), C2 = C([0,52]), C3 = C1 + C2 = C([0,51]), and C∩ = C1 ∩ C2 = C([253,52]) 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(1690, 255, F16, 53) (dual of [255, 165, 54]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,52], and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(1694, 255, F16, 55) (dual of [255, 161, 56]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−2,−1,…,52}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(1688, 255, F16, 52) (dual of [255, 167, 53]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,51], and designed minimum distance d ≥ |I|+1 = 53 [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
- linear OA(160, 2, F16, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(1695, 131, F16, 2, 55) (dual of [(131, 2), 167, 56]-NRT-code) | [i] | OOA Folding | |