Information on Result #2270480
Linear OA(467, 65556, F4, 11) (dual of [65556, 65489, 12]-code), using 1 times code embedding in larger space based on linear OA(466, 65555, F4, 11) (dual of [65555, 65489, 12]-code), using
- construction X4 applied to C([0,5]) ⊂ C([0,4]) [i] based on
- linear OA(465, 65537, F4, 11) (dual of [65537, 65472, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(449, 65537, F4, 9) (dual of [65537, 65488, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(417, 18, F4, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,4)), using
- dual of repetition code with length 18 [i]
- linear OA(41, 18, F4, 1) (dual of [18, 17, 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(467, 35947, F4, 2, 11) (dual of [(35947, 2), 71827, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(467, 35947, F4, 3, 11) (dual of [(35947, 3), 107774, 12]-NRT-code) | [i] | ||
| 3 | Digital (56, 67, 35947)-net over F4 | [i] | ||
| 4 | Linear OOA(467, 32778, F4, 2, 11) (dual of [(32778, 2), 65489, 12]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(467, 21852, F4, 3, 11) (dual of [(21852, 3), 65489, 12]-NRT-code) | [i] | ||
| 6 | Linear OOA(467, 13111, F4, 11, 11) (dual of [(13111, 11), 144154, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |