Information on Result #2487481
Linear OOA(3211, 29544, F3, 2, 31) (dual of [(29544, 2), 58877, 32]-NRT-code), using 31 times duplication based on linear OOA(3210, 29544, F3, 2, 31) (dual of [(29544, 2), 58878, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3210, 59088, F3, 31) (dual of [59088, 58878, 32]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3209, 59087, F3, 31) (dual of [59087, 58878, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- linear OA(3201, 59049, F3, 31) (dual of [59049, 58848, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(30) ⊂ Ce(25) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3209, 59087, F3, 31) (dual of [59087, 58878, 32]-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(3211, 20548, F3, 3, 31) (dual of [(20548, 3), 61433, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3211, 20548, F3, 4, 31) (dual of [(20548, 4), 81981, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(3211, 20548, F3, 5, 31) (dual of [(20548, 5), 102529, 32]-NRT-code) | [i] | ||
| 4 | Digital (180, 211, 20548)-net over F3 | [i] | ||