Information on Result #2487777
Linear OOA(3231, 29544, F3, 2, 34) (dual of [(29544, 2), 58857, 35]-NRT-code), using 31 times duplication based on linear OOA(3230, 29544, F3, 2, 34) (dual of [(29544, 2), 58858, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3230, 59088, F3, 34) (dual of [59088, 58858, 35]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3229, 59087, F3, 34) (dual of [59087, 58858, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- linear OA(3221, 59049, F3, 34) (dual of [59049, 58828, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(3191, 59049, F3, 29) (dual of [59049, 58858, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(38, 38, F3, 4) (dual of [38, 30, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3229, 59087, F3, 34) (dual of [59087, 58858, 35]-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(3231, 20745, F3, 3, 34) (dual of [(20745, 3), 62004, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3231, 20745, F3, 4, 34) (dual of [(20745, 4), 82749, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(3231, 20745, F3, 5, 34) (dual of [(20745, 5), 103494, 35]-NRT-code) | [i] | ||
| 4 | Digital (197, 231, 20745)-net over F3 | [i] | ||