Information on Result #678089
Linear OA(4129, 1048625, F4, 16) (dual of [1048625, 1048496, 17]-code), using construction X applied to C([0,8]) ⊂ C([0,5]) based on
- linear OA(4121, 1048577, F4, 17) (dual of [1048577, 1048456, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(481, 1048577, F4, 11) (dual of [1048577, 1048496, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 420−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(48, 48, F4, 4) (dual of [48, 40, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 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(4129, 643988, F4, 2, 16) (dual of [(643988, 2), 1287847, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4129, 643988, F4, 3, 16) (dual of [(643988, 3), 1931835, 17]-NRT-code) | [i] | ||
| 3 | Digital (113, 129, 643988)-net over F4 | [i] | ||
| 4 | Linear OOA(4129, 524312, F4, 2, 16) (dual of [(524312, 2), 1048495, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4129, 349541, F4, 3, 16) (dual of [(349541, 3), 1048494, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(4129, 131078, F4, 16, 16) (dual of [(131078, 16), 2097119, 17]-NRT-code) | [i] | OA Folding and Stacking | |