Information on Result #1301269
Linear OA(533, 15635, F5, 7) (dual of [15635, 15602, 8]-code), using construction X with Varšamov bound based on
- linear OA(532, 15633, F5, 7) (dual of [15633, 15601, 8]-code), using
- construction X4 applied to C([0,6]) ⊂ C([1,5]) [i] based on
- linear OA(531, 15624, F5, 7) (dual of [15624, 15593, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(524, 15624, F5, 5) (dual of [15624, 15600, 6]-code), using the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(58, 9, F5, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,5)), using
- dual of repetition code with length 9 [i]
- linear OA(51, 9, F5, 1) (dual of [9, 8, 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
- construction X4 applied to C([0,6]) ⊂ C([1,5]) [i] based on
- linear OA(532, 15634, F5, 6) (dual of [15634, 15602, 7]-code), using Gilbert–Varšamov bound and bm = 532 > Vbs−1(k−1) = 7963 193201 638366 341829 [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(533, 15635, F5, 2, 7) (dual of [(15635, 2), 31237, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(533, 15635, F5, 3, 7) (dual of [(15635, 3), 46872, 8]-NRT-code) | [i] | ||
| 3 | Digital (26, 33, 15635)-net over F5 | [i] | ||