Information on Result #823322
Linear OOA(4114, 131088, F4, 2, 17) (dual of [(131088, 2), 262062, 18]-NRT-code), using OOA 2-folding based on linear OA(4114, 262176, F4, 17) (dual of [262176, 262062, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(4109, 262144, F4, 17) (dual of [262144, 262035, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(482, 262144, F4, 13) (dual of [262144, 262062, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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 OOA(4116, 131089, F4, 2, 17) (dual of [(131089, 2), 262062, 18]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(4118, 131090, F4, 2, 17) (dual of [(131090, 2), 262062, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(4115, 131088, F4, 2, 17) (dual of [(131088, 2), 262061, 18]-NRT-code) | [i] | OOA Duplication | |
| 4 | Linear OOA(4114, 131088, F4, 3, 17) (dual of [(131088, 3), 393150, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (97, 114, 131088)-net over F4 | [i] | ||