Information on Result #1429543
Linear OOA(4209, 45321, F4, 2, 33) (dual of [(45321, 2), 90433, 34]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4209, 45321, F4, 33) (dual of [45321, 45112, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(4209, 65554, F4, 33) (dual of [65554, 65345, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([1,16]) [i] based on
- linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4192, 65537, F4, 16) (dual of [65537, 65345, 17]-code), using the narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(416, 17, F4, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,4)), using
- dual of repetition code with length 17 [i]
- construction X applied to C([0,16]) ⊂ C([1,16]) [i] based on
Mode: 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(4209, 22660, F4, 3, 33) (dual of [(22660, 3), 67771, 34]-NRT-code) | [i] | OOA Folding | |