Information on Result #682657
Linear OA(519, 15631, F5, 4) (dual of [15631, 15612, 5]-code), using construction X applied to Ce(3) ⊂ Ce(2) based on
- linear OA(519, 15625, F5, 4) (dual of [15625, 15606, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(513, 15625, F5, 3) (dual of [15625, 15612, 4]-code or 15625-cap in PG(12,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(50, 6, F5, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 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(519, 15631, F5, 2, 4) (dual of [(15631, 2), 31243, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(519, 15631, F5, 3, 4) (dual of [(15631, 3), 46874, 5]-NRT-code) | [i] | ||
| 3 | Linear OOA(519, 7815, F5, 2, 4) (dual of [(7815, 2), 15611, 5]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(519, 7815, F5, 3, 4) (dual of [(7815, 3), 23426, 5]-NRT-code) | [i] | OA Folding and Stacking | |