Information on Result #694281
Linear OA(2587, 648, F25, 42) (dual of [648, 561, 43]-code), using construction X applied to Ce(41) ⊂ Ce(33) based on
- linear OA(2580, 625, F25, 42) (dual of [625, 545, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2564, 625, F25, 34) (dual of [625, 561, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(257, 23, F25, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,25)), using
- discarding factors / shortening the dual code based on linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)), using
- Reed–Solomon code RS(18,25) [i]
- discarding factors / shortening the dual code based on linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)), 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(2587, 647, F25, 2, 42) (dual of [(647, 2), 1207, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (45, 87, 647)-net over F25 | [i] | ||
| 3 | Linear OOA(2587, 324, F25, 2, 42) (dual of [(324, 2), 561, 43]-NRT-code) | [i] | OOA Folding | |