Information on Result #693509
Linear OA(2557, 15636, F25, 19) (dual of [15636, 15579, 20]-code), using construction X applied to Ce(18) ⊂ Ce(15) based on
- linear OA(2555, 15625, F25, 19) (dual of [15625, 15570, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2546, 15625, F25, 16) (dual of [15625, 15579, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(252, 11, F25, 2) (dual of [11, 9, 3]-code or 11-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
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(2557, 12034, F25, 2, 19) (dual of [(12034, 2), 24011, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (38, 57, 12034)-net over F25 | [i] | ||
| 3 | Linear OOA(2557, 7818, F25, 2, 19) (dual of [(7818, 2), 15579, 20]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2557, 1737, F25, 19, 19) (dual of [(1737, 19), 32946, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |