Information on Result #814173
Linear OOA(3166, 29538, F3, 2, 24) (dual of [(29538, 2), 58910, 25]-NRT-code), using OOA 2-folding based on linear OA(3166, 59076, F3, 24) (dual of [59076, 58910, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3166, 59077, F3, 24) (dual of [59077, 58911, 25]-code), using
- construction XX applied to Ce(24) ⊂ Ce(21) ⊂ Ce(19) [i] based on
- linear OA(3161, 59049, F3, 25) (dual of [59049, 58888, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3141, 59049, F3, 22) (dual of [59049, 58908, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3131, 59049, F3, 20) (dual of [59049, 58918, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(31, 24, F3, 1) (dual of [24, 23, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(31, 4, F3, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
- construction XX applied to Ce(24) ⊂ Ce(21) ⊂ Ce(19) [i] based on
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(3166, 23077, F3, 3, 24) (dual of [(23077, 3), 69065, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3166, 23077, F3, 4, 24) (dual of [(23077, 4), 92142, 25]-NRT-code) | [i] | ||
| 3 | Linear OOA(3166, 23077, F3, 5, 24) (dual of [(23077, 5), 115219, 25]-NRT-code) | [i] | ||
| 4 | Digital (142, 166, 23077)-net over F3 | [i] | ||