Information on Result #723620
Linear OA(2545, 634, F25, 22) (dual of [634, 589, 23]-code), using construction XX applied to C1 = C([621,17]), C2 = C([0,18]), C3 = C1 + C2 = C([0,17]), and C∩ = C1 ∩ C2 = C([621,18]) based on
- linear OA(2541, 624, F25, 21) (dual of [624, 583, 22]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,17}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2537, 624, F25, 19) (dual of [624, 587, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2543, 624, F25, 22) (dual of [624, 581, 23]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,18}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2535, 624, F25, 18) (dual of [624, 589, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [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 OA(2560, 700, F25, 22) (dual of [700, 640, 23]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2561, 702, F25, 22) (dual of [702, 641, 23]-code) | [i] | ||
| 3 | Linear OOA(2545, 317, F25, 2, 22) (dual of [(317, 2), 589, 23]-NRT-code) | [i] | OOA Folding | |