Information on Result #721803
Linear OA(1676, 262, F16, 42) (dual of [262, 186, 43]-code), using construction XX applied to C1 = C([253,38]), C2 = C([0,39]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([253,39]) based on
- linear OA(1673, 255, F16, 41) (dual of [255, 182, 42]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−2,−1,…,38}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(1671, 255, F16, 40) (dual of [255, 184, 41]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,39], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(1675, 255, F16, 42) (dual of [255, 180, 43]-code), using the primitive BCH-code C(I) with length 255 = 162−1, defining interval I = {−2,−1,…,39}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(1669, 255, F16, 39) (dual of [255, 186, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [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(1676, 131, F16, 2, 42) (dual of [(131, 2), 186, 43]-NRT-code) | [i] | OOA Folding | |