Information on Result #824432
Linear OOA(4182, 131082, F4, 2, 27) (dual of [(131082, 2), 261982, 28]-NRT-code), using OOA 2-folding based on linear OA(4182, 262164, F4, 27) (dual of [262164, 261982, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(4181, 262145, F4, 27) (dual of [262145, 261964, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(4163, 262145, F4, 25) (dual of [262145, 261982, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [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
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(4184, 131083, F4, 2, 27) (dual of [(131083, 2), 261982, 28]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(4183, 131082, F4, 2, 27) (dual of [(131082, 2), 261981, 28]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(4182, 107057, F4, 3, 27) (dual of [(107057, 3), 320989, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (155, 182, 107057)-net over F4 | [i] | ||