Information on Result #677882
Linear OA(4141, 4194357, F4, 16) (dual of [4194357, 4194216, 17]-code), using construction X applied to C([0,8]) ⊂ C([0,5]) based on
- linear OA(4133, 4194305, F4, 17) (dual of [4194305, 4194172, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(489, 4194305, F4, 11) (dual of [4194305, 4194216, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(48, 52, F4, 4) (dual of [52, 44, 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(4141, 2113169, F4, 2, 16) (dual of [(2113169, 2), 4226197, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4141, 2113169, F4, 3, 16) (dual of [(2113169, 3), 6339366, 17]-NRT-code) | [i] | ||
| 3 | Digital (125, 141, 2113169)-net over F4 | [i] | ||
| 4 | Linear OOA(4141, 2097178, F4, 2, 16) (dual of [(2097178, 2), 4194215, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4141, 1398119, F4, 3, 16) (dual of [(1398119, 3), 4194216, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(4141, 524294, F4, 16, 16) (dual of [(524294, 16), 8388563, 17]-NRT-code) | [i] | OA Folding and Stacking | |