Information on Result #694822
Linear OA(2713, 531445, F27, 4) (dual of [531445, 531432, 5]-code), using construction X applied to Ce(3) ⊂ Ce(2) based on
- linear OA(2713, 531441, F27, 4) (dual of [531441, 531428, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(279, 531441, F27, 3) (dual of [531441, 531432, 4]-code or 531441-cap in PG(8,27)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(270, 4, F27, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 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(2715, 531473, F27, 4) (dual of [531473, 531458, 5]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(2713, 531445, F27, 2, 4) (dual of [(531445, 2), 1062877, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (9, 13, 531445)-net over F27 | [i] | ||
| 4 | Linear OOA(2713, 265722, F27, 2, 4) (dual of [(265722, 2), 531431, 5]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2713, 265722, F27, 4, 4) (dual of [(265722, 4), 1062875, 5]-NRT-code) | [i] | OA Folding and Stacking | |