Information on Result #2271246
Linear OA(4105, 65577, F4, 16) (dual of [65577, 65472, 17]-code), using 1 times code embedding in larger space based on linear OA(4104, 65576, F4, 16) (dual of [65576, 65472, 17]-code), using
- construction X applied to C([0,8]) ⊂ C([0,5]) [i] based on
- linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- 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(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-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(4105, 59800, F4, 2, 16) (dual of [(59800, 2), 119495, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4105, 59800, F4, 3, 16) (dual of [(59800, 3), 179295, 17]-NRT-code) | [i] | ||
| 3 | Digital (89, 105, 59800)-net over F4 | [i] | ||
| 4 | Linear OOA(4105, 21859, F4, 3, 16) (dual of [(21859, 3), 65472, 17]-NRT-code) | [i] | OOA Folding | |