Information on Result #1301504
Linear OA(580, 15659, F5, 15) (dual of [15659, 15579, 16]-code), using construction X with Varšamov bound based on
- linear OA(578, 15655, F5, 15) (dual of [15655, 15577, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,5]) [i] based on
- linear OA(573, 15626, F5, 15) (dual of [15626, 15553, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(549, 15626, F5, 11) (dual of [15626, 15577, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(55, 29, F5, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- construction X applied to C([0,7]) ⊂ C([0,5]) [i] based on
- linear OA(578, 15657, F5, 14) (dual of [15657, 15579, 15]-code), using Gilbert–Varšamov bound and bm = 578 > Vbs−1(k−1) = 36414 645419 717975 589858 772363 055759 268814 797924 073825 [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 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(580, 15659, F5, 2, 15) (dual of [(15659, 2), 31238, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(580, 15659, F5, 3, 15) (dual of [(15659, 3), 46897, 16]-NRT-code) | [i] | ||
| 3 | Digital (65, 80, 15659)-net over F5 | [i] | ||