Information on Result #730963
Linear OA(520, 31256, F5, 4) (dual of [31256, 31236, 5]-code), using trace code based on linear OA(2510, 15628, F25, 4) (dual of [15628, 15618, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(2510, 15625, F25, 4) (dual of [15625, 15615, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(257, 15625, F25, 3) (dual of [15625, 15618, 4]-code or 15625-cap in PG(6,25)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(250, 3, F25, 0) (dual of [3, 3, 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 OA(521, 31257, F5, 4) (dual of [31257, 31236, 5]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(520, 31256, F5, 2, 4) (dual of [(31256, 2), 62492, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(520, 31256, F5, 3, 4) (dual of [(31256, 3), 93748, 5]-NRT-code) | [i] | ||
| 4 | Linear OOA(520, 15628, F5, 2, 4) (dual of [(15628, 2), 31236, 5]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(520, 15628, F5, 3, 4) (dual of [(15628, 3), 46864, 5]-NRT-code) | [i] | OA Folding and Stacking | |