Information on Result #723036
Linear OA(25107, 322, F25, 59) (dual of [322, 215, 60]-code), using construction XX applied to C1 = C([309,54]), C2 = C([0,55]), C3 = C1 + C2 = C([0,54]), and C∩ = C1 ∩ C2 = C([309,55]) based on
- linear OA(25103, 312, F25, 58) (dual of [312, 209, 59]-code), using the BCH-code C(I) with length 312 | 252−1, defining interval I = {−3,−2,…,54}, and designed minimum distance d ≥ |I|+1 = 59 [i]
- linear OA(2599, 312, F25, 56) (dual of [312, 213, 57]-code), using the expurgated narrow-sense BCH-code C(I) with length 312 | 252−1, defining interval I = [0,55], and designed minimum distance d ≥ |I|+1 = 57 [i]
- linear OA(25105, 312, F25, 59) (dual of [312, 207, 60]-code), using the BCH-code C(I) with length 312 | 252−1, defining interval I = {−3,−2,…,55}, and designed minimum distance d ≥ |I|+1 = 60 [i]
- linear OA(2597, 312, F25, 55) (dual of [312, 215, 56]-code), using the expurgated narrow-sense BCH-code C(I) with length 312 | 252−1, defining interval I = [0,54], and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(252, 8, F25, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 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(25107, 161, F25, 2, 59) (dual of [(161, 2), 215, 60]-NRT-code) | [i] | OOA Folding | |