Information on Result #2496097
Linear OOA(4157, 131082, F4, 2, 23) (dual of [(131082, 2), 262007, 24]-NRT-code), using 41 times duplication based on linear OOA(4156, 131082, F4, 2, 23) (dual of [(131082, 2), 262008, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4156, 262164, F4, 23) (dual of [262164, 262008, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4155, 262163, F4, 23) (dual of [262163, 262008, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(4154, 262144, F4, 23) (dual of [262144, 261990, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(41, 19, F4, 1) (dual of [19, 18, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4155, 262163, F4, 23) (dual of [262163, 262008, 24]-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(4157, 128262, F4, 3, 23) (dual of [(128262, 3), 384629, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (134, 157, 128262)-net over F4 | [i] | ||