Information on Result #2288104
Linear OA(25102, 15654, F25, 33) (dual of [15654, 15552, 34]-code), using 1 times code embedding in larger space based on linear OA(25101, 15653, F25, 33) (dual of [15653, 15552, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(25) [i] based on
- linear OA(2594, 15625, F25, 33) (dual of [15625, 15531, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2573, 15625, F25, 26) (dual of [15625, 15552, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(257, 28, F25, 6) (dual of [28, 21, 7]-code), using
- construction X applied to RS(19,25) ⊂ RS(21,25) [i] based on
- linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), using Reed–Solomon code RS(19,25) [i]
- 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]
- linear OA(251, 3, F25, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to RS(19,25) ⊂ RS(21,25) [i] based on
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(25102, 7827, F25, 2, 33) (dual of [(7827, 2), 15552, 34]-NRT-code) | [i] | OOA Folding | |