Information on Result #2495855
Linear OOA(4144, 131089, F4, 2, 21) (dual of [(131089, 2), 262034, 22]-NRT-code), using 41 times duplication based on linear OOA(4143, 131089, F4, 2, 21) (dual of [(131089, 2), 262035, 22]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4141, 131088, F4, 2, 21) (dual of [(131088, 2), 262035, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4141, 262176, F4, 21) (dual of [262176, 262035, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 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(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
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- OOA 2-folding [i] based on linear OA(4141, 262176, F4, 21) (dual of [262176, 262035, 22]-code), 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(4144, 131089, F4, 3, 21) (dual of [(131089, 3), 393123, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (123, 144, 131089)-net over F4 | [i] | ||