Information on Result #723330
Linear OA(2539, 640, F25, 18) (dual of [640, 601, 19]-code), using construction XX applied to C1 = C([619,11]), C2 = C([0,12]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C([619,12]) based on
- linear OA(2533, 624, F25, 17) (dual of [624, 591, 18]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−5,−4,…,11}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2525, 624, F25, 13) (dual of [624, 599, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2535, 624, F25, 18) (dual of [624, 589, 19]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−5,−4,…,12}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2523, 624, F25, 12) (dual of [624, 601, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(254, 14, F25, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), 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(2539, 320, F25, 2, 18) (dual of [(320, 2), 601, 19]-NRT-code) | [i] | OOA Folding | |