Information on Result #694841
Linear OA(2714, 531451, F27, 4) (dual of [531451, 531437, 5]-code), using construction X4 applied to Ce(3) ⊂ Ce(1) 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(275, 531441, F27, 2) (dual of [531441, 531436, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(279, 10, F27, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,27)), using
- dual of repetition code with length 10 [i]
- linear OA(271, 10, F27, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code), using
- Reed–Solomon code RS(26,27) [i]
- discarding factors / shortening the dual code based on linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code), 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(2714, 531451, F27, 2, 4) (dual of [(531451, 2), 1062888, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (10, 14, 531451)-net over F27 | [i] | ||