Information on Result #1301243
Linear OA(527, 31258, F5, 5) (dual of [31258, 31231, 6]-code), using construction X with Varšamov bound based on
- linear OA(526, 31256, F5, 5) (dual of [31256, 31230, 6]-code), using
- trace code [i] based on linear OA(2513, 15628, F25, 5) (dual of [15628, 15615, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(2513, 15625, F25, 5) (dual of [15625, 15612, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- 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(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
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- trace code [i] based on linear OA(2513, 15628, F25, 5) (dual of [15628, 15615, 6]-code), using
- linear OA(526, 31257, F5, 4) (dual of [31257, 31231, 5]-code), using Gilbert–Varšamov bound and bm = 526 > Vbs−1(k−1) = 325 684923 376545 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 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: 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(527, 31258, F5, 2, 5) (dual of [(31258, 2), 62489, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(527, 31258, F5, 3, 5) (dual of [(31258, 3), 93747, 6]-NRT-code) | [i] | ||
| 3 | Digital (22, 27, 31258)-net over F5 | [i] | ||
| 4 | Linear OOA(527, 15629, F5, 2, 5) (dual of [(15629, 2), 31231, 6]-NRT-code) | [i] | OOA Folding | |