Information on Result #683231
Linear OA(527, 3132, F5, 7) (dual of [3132, 3105, 8]-code), using construction X4 applied to C([0,6]) ⊂ C([1,5]) based on
- linear OA(526, 3124, F5, 7) (dual of [3124, 3098, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(520, 3124, F5, 5) (dual of [3124, 3104, 6]-code), using the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(57, 8, F5, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,5)), using
- dual of repetition code with length 8 [i]
- linear OA(51, 8, F5, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-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 OOA(527, 2805, F5, 2, 7) (dual of [(2805, 2), 5583, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(527, 2805, F5, 3, 7) (dual of [(2805, 3), 8388, 8]-NRT-code) | [i] | ||
| 3 | Digital (20, 27, 2805)-net over F5 | [i] | ||
| 4 | Linear OA(528, 3134, F5, 7) (dual of [3134, 3106, 8]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(527, 1566, F5, 2, 7) (dual of [(1566, 2), 3105, 8]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(527, 1044, F5, 3, 7) (dual of [(1044, 3), 3105, 8]-NRT-code) | [i] | ||