Information on Result #731597
Linear OA(1676, 131094, F16, 18) (dual of [131094, 131018, 19]-code), using trace code based on linear OA(25638, 65547, F256, 18) (dual of [65547, 65509, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(1677, 131095, F16, 18) (dual of [131095, 131018, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1676, 131094, F16, 2, 18) (dual of [(131094, 2), 262112, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (58, 76, 131094)-net over F16 | [i] | ||
| 4 | Linear OOA(1676, 65547, F16, 2, 18) (dual of [(65547, 2), 131018, 19]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(1676, 14566, F16, 18, 18) (dual of [(14566, 18), 262112, 19]-NRT-code) | [i] | OA Folding and Stacking | |