Information on Result #1301644
Linear OA(599, 15659, F5, 19) (dual of [15659, 15560, 20]-code), using construction X with Varšamov bound based on
- linear OA(597, 15655, F5, 19) (dual of [15655, 15558, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(567, 15625, F5, 14) (dual of [15625, 15558, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(597, 15657, F5, 18) (dual of [15657, 15560, 19]-code), using Gilbert–Varšamov bound and bm = 597 > Vbs−1(k−1) = 9 769430 352196 381753 561125 904092 064489 021480 151655 493943 719775 568225 [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(599, 15659, F5, 2, 19) (dual of [(15659, 2), 31219, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(599, 15659, F5, 3, 19) (dual of [(15659, 3), 46878, 20]-NRT-code) | [i] | ||
| 3 | Digital (80, 99, 15659)-net over F5 | [i] | ||