Information on Result #731653
Linear OA(16108, 131094, F16, 26) (dual of [131094, 130986, 27]-code), using trace code based on linear OA(25654, 65547, F256, 26) (dual of [65547, 65493, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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
Mode: Constructive and 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 OA(16109, 131095, F16, 26) (dual of [131095, 130986, 27]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(16108, 131094, F16, 2, 26) (dual of [(131094, 2), 262080, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (82, 108, 131094)-net over F16 | [i] | ||
| 4 | Linear OA(16109, 131096, F16, 26) (dual of [131096, 130987, 27]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(16108, 65547, F16, 2, 26) (dual of [(65547, 2), 130986, 27]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(16108, 10084, F16, 26, 26) (dual of [(10084, 26), 262076, 27]-NRT-code) | [i] | OA Folding and Stacking | |