Information on Result #694821
Linear OA(2717, 531445, F27, 5) (dual of [531445, 531428, 6]-code), using construction X applied to Ce(4) ⊂ Ce(3) based on
- linear OA(2717, 531441, F27, 5) (dual of [531441, 531424, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- 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(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(2719, 531473, F27, 5) (dual of [531473, 531454, 6]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2720, 532202, F27, 5) (dual of [532202, 532182, 6]-code) | [i] | ||
| 3 | Linear OOA(2717, 531445, F27, 2, 5) (dual of [(531445, 2), 1062873, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (12, 17, 531445)-net over F27 | [i] | ||
| 5 | Linear OOA(2717, 265722, F27, 2, 5) (dual of [(265722, 2), 531427, 6]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2717, 265722, F27, 5, 5) (dual of [(265722, 5), 1328593, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |