Information on Result #1303709
Linear OA(1685, 131096, F16, 20) (dual of [131096, 131011, 21]-code), using construction X with Varšamov bound based on
- linear OA(1684, 131094, F16, 20) (dual of [131094, 131010, 21]-code), using
- trace code [i] based on linear OA(25642, 65547, F256, 20) (dual of [65547, 65505, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- trace code [i] based on linear OA(25642, 65547, F256, 20) (dual of [65547, 65505, 21]-code), using
- linear OA(1684, 131095, F16, 19) (dual of [131095, 131011, 20]-code), using Gilbert–Varšamov bound and bm = 1684 > Vbs−1(k−1) = 30 150144 744904 567339 565223 178212 850727 005615 763222 181944 173811 420298 785575 716694 054040 947598 558386 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 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(1685, 131096, F16, 2, 20) (dual of [(131096, 2), 262107, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (65, 85, 131096)-net over F16 | [i] | ||
| 3 | Linear OOA(1685, 65548, F16, 2, 20) (dual of [(65548, 2), 131011, 21]-NRT-code) | [i] | OOA Folding | |