Information on Result #823500
Linear OOA(4129, 131083, F4, 2, 19) (dual of [(131083, 2), 262037, 20]-NRT-code), using OOA 2-folding based on linear OA(4129, 262166, F4, 19) (dual of [262166, 262037, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4128, 262165, F4, 19) (dual of [262165, 262037, 20]-code), using
- construction X4 applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(4127, 262145, F4, 19) (dual of [262145, 262018, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(4109, 262145, F4, 17) (dual of [262145, 262036, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(419, 20, F4, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,4)), using
- dual of repetition code with length 20 [i]
- linear OA(41, 20, F4, 1) (dual of [20, 19, 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 X4 applied to C([0,9]) ⊂ C([0,8]) [i] based on
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(4131, 131084, F4, 2, 19) (dual of [(131084, 2), 262037, 20]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(4130, 131083, F4, 2, 19) (dual of [(131083, 2), 262036, 20]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(4129, 131083, F4, 3, 19) (dual of [(131083, 3), 393120, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (110, 129, 131083)-net over F4 | [i] | ||