Information on Result #678586
Linear OA(4104, 65576, F4, 16) (dual of [65576, 65472, 17]-code), using construction X applied to C([0,8]) ⊂ C([0,5]) 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 OA(4105, 65577, F4, 16) (dual of [65577, 65472, 17]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4104, 54162, F4, 2, 16) (dual of [(54162, 2), 108220, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(4104, 54162, F4, 3, 16) (dual of [(54162, 3), 162382, 17]-NRT-code) | [i] | ||
| 4 | Digital (88, 104, 54162)-net over F4 | [i] | ||
| 5 | Linear OA(4106, 65579, F4, 16) (dual of [65579, 65473, 17]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(4104, 32788, F4, 2, 16) (dual of [(32788, 2), 65472, 17]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4104, 21858, F4, 3, 16) (dual of [(21858, 3), 65470, 17]-NRT-code) | [i] | ||
| 8 | Linear OOA(4104, 8197, F4, 16, 16) (dual of [(8197, 16), 131048, 17]-NRT-code) | [i] | OA Folding and Stacking | |