Information on Result #693568
Linear OA(2541, 15644, F25, 13) (dual of [15644, 15603, 14]-code), using construction X applied to Ce(12) ⊂ Ce(7) based on
- linear OA(2537, 15625, F25, 13) (dual of [15625, 15588, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2522, 15625, F25, 8) (dual of [15625, 15603, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(254, 19, F25, 4) (dual of [19, 15, 5]-code or 19-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
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(2541, 15644, F25, 2, 13) (dual of [(15644, 2), 31247, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (28, 41, 15644)-net over F25 | [i] | ||
| 3 | Linear OOA(2541, 7822, F25, 2, 13) (dual of [(7822, 2), 15603, 14]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2541, 2607, F25, 13, 13) (dual of [(2607, 13), 33850, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |