Information on Result #1301829
Linear OA(5129, 15661, F5, 25) (dual of [15661, 15532, 26]-code), using construction X with Varšamov bound based on
- linear OA(5126, 15655, F5, 25) (dual of [15655, 15529, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(5121, 15626, F5, 25) (dual of [15626, 15505, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(597, 15626, F5, 21) (dual of [15626, 15529, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(5126, 15658, F5, 24) (dual of [15658, 15532, 25]-code), using Gilbert–Varšamov bound and bm = 5126 > Vbs−1(k−1) = 8059 734121 036755 287755 417156 405299 618310 630872 118951 505682 086324 776670 208590 780426 487525 [i]
- linear OA(50, 3, F5, 0) (dual of [3, 3, 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(5129, 15661, F5, 2, 25) (dual of [(15661, 2), 31193, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5129, 15661, F5, 3, 25) (dual of [(15661, 3), 46854, 26]-NRT-code) | [i] | ||
| 3 | Digital (104, 129, 15661)-net over F5 | [i] | ||
| 4 | Linear OOA(5129, 7830, F5, 2, 25) (dual of [(7830, 2), 15531, 26]-NRT-code) | [i] | OOA Folding | |