Information on Result #678554
Linear OA(4100, 65556, F4, 16) (dual of [65556, 65456, 17]-code), using construction X applied to C([0,8]) ⊂ C([0,6]) 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(481, 65537, F4, 13) (dual of [65537, 65456, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(43, 19, F4, 2) (dual of [19, 16, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-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(4100, 36445, F4, 2, 16) (dual of [(36445, 2), 72790, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4100, 36445, F4, 3, 16) (dual of [(36445, 3), 109235, 17]-NRT-code) | [i] | ||
| 3 | Digital (84, 100, 36445)-net over F4 | [i] | ||
| 4 | Linear OOA(4100, 21852, F4, 3, 16) (dual of [(21852, 3), 65456, 17]-NRT-code) | [i] | OOA Folding | |