Information on Result #730500
Linear OA(12837, 390, F128, 21) (dual of [390, 353, 22]-code), using construction XX applied to C1 = C([378,16]), C2 = C([0,17]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([378,17]) based on
- linear OA(12833, 381, F128, 20) (dual of [381, 348, 21]-code), using the BCH-code C(I) with length 381 | 1282−1, defining interval I = {−3,−2,…,16}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(12830, 381, F128, 18) (dual of [381, 351, 19]-code), using the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(12835, 381, F128, 21) (dual of [381, 346, 22]-code), using the BCH-code C(I) with length 381 | 1282−1, defining interval I = {−3,−2,…,17}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12828, 381, F128, 17) (dual of [381, 353, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1282, 7, F128, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 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(12837, 195, F128, 2, 21) (dual of [(195, 2), 353, 22]-NRT-code) | [i] | OOA Folding | |