Information on Result #1523319
Linear OOA(3132, 25578, F3, 3, 19) (dual of [(25578, 3), 76602, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3132, 25578, F3, 2, 19) (dual of [(25578, 2), 51024, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3132, 29550, F3, 2, 19) (dual of [(29550, 2), 58968, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3132, 59100, F3, 19) (dual of [59100, 58968, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3132, 59101, F3, 19) (dual of [59101, 58969, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,6]) [i] based on
- linear OA(3121, 59050, F3, 19) (dual of [59050, 58929, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(381, 59050, F3, 13) (dual of [59050, 58969, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(311, 51, F3, 5) (dual of [51, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to C([0,9]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3132, 59101, F3, 19) (dual of [59101, 58969, 20]-code), using
- OOA 2-folding [i] based on linear OA(3132, 59100, F3, 19) (dual of [59100, 58968, 20]-code), using
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(3132, 12789, F3, 5, 19) (dual of [(12789, 5), 63813, 20]-NRT-code) | [i] | OOA Folding | |